400 ejercicios sobre Operaciones entre Conjuntos con sus soluciones.

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Operaciones entre conjuntos
Resolver las operaciones indicadas:
1). Dado el conjunto universal:
y los subconjuntos:
2). Dado el conjunto universal:
y los subconjuntos:
3). Dado el conjunto universal:
y los subconjuntos:
4). Dado el conjunto universal:
y los subconjuntos:
5). Dado el conjunto universal:
y los subconjuntos:
6). Dado el conjunto universal:
y los subconjuntos:
7). Dado el conjunto universal:
y los subconjuntos:
8). Dado el conjunto universal:
y los subconjuntos:
9). Dado el conjunto universal:
y los subconjuntos:
10). Dado el conjunto universal:
y los subconjuntos:
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 3, 5, 7, 11, 13, 17, 19, 31}
= {2, 7, 11, 13, 19, 23, 37}
Hallar:  ( ∪ ) ∩A, ∩ ( −A)Bc Cc Bc Cc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 30, 60, 70, 90}
= {10, 20, 30, 50, 60, 70, 90, 100}
= {10, 30, 40, 50, 60, 70, 80}
Hallar:  (A∩ ) − , A∩ ( △ )Cc Bc Cc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 8, 12, 28, 36, 44}
= {4, 8, 12, 16, 24, 28, 32, 36, 44, 48}
= {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
Hallar:  (B△A) ∪C, B∪ (A∩C)
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {6, 9, 12, 18, 21, 24, 30, 33, 36}
= {9, 15, 18, 24, 27, 36}
= {6, 9, 15, 18, 36}
Hallar:  (C∪A) ∩B, C− (A∪B)
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 10, 15, 20, 25, 45, 55, 60}
= {5, 15, 20, 40, 50, 60}
= {5, 10, 15, 30, 35, 45}
Hallar:  (C△ ) − , C∪ ( △ )Bc Ac Bc Ac
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {16, 24, 32, 56, 72, 88, 96}
= {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
= {8, 16, 24, 32, 40, 48, 64, 72, 80, 88, 96}
Hallar:  ( − )△C, ∪ ( ∩C)Ac Bc Ac Bc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 60, 70, 80, 100}
= {10, 20, 40, 80, 90}
= {10, 20, 30, 40, 60, 70, 90, 100}
Hallar:  ( ∩ ) ∩ , ∩ ( ∪ )Bc Cc Ac Bc Cc Ac
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 8, 12, 16, 20, 28, 32, 36, 40, 44, 48}
= {8, 12, 16, 20, 28, 40, 44}
= {4, 8, 12, 16, 20, 28, 32, 40, 44, 48}
Hallar:  (C∩B) ∪A, C△ (B△A)
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 72, 84, 96}
= {24, 36, 48, 60, 72, 84, 120}
= {24, 36, 60, 72, 96}
Hallar:  ( − ) ∪B, △ ( ∩B)A
c Cc Ac Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 9, 12, 15, 18, 21, 24, 30, 33, 36}
= {9, 12, 15, 18, 21, 30, 33}
= {3, 6, 9, 12, 18, 21, 24, 27, 30, 33, 36}
Hallar:  (A△ )△C, A∩ ( ∪C)Bc Bc
11). Dado el conjunto universal:
y los subconjuntos:
12). Dado el conjunto universal:
y los subconjuntos:
13). Dado el conjunto universal:
y los subconjuntos:
14). Dado el conjunto universal:
y los subconjuntos:
15). Dado el conjunto universal:
y los subconjuntos:
16). Dado el conjunto universal:
y los subconjuntos:
17). Dado el conjunto universal:
y los subconjuntos:
18). Dado el conjunto universal:
y los subconjuntos:
19). Dado el conjunto universal:
y los subconjuntos:
20). Dado el conjunto universal:
y los subconjuntos:
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 4, 6, 10, 14, 16, 18, 20}
= {4, 6, 8, 10, 12, 14, 16, 18, 20, 22}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Hallar:  ( − ) ∩C, − ( ∩C)Bc Ac Bc Ac
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {20, 30, 40, 60, 70, 90}
= {10, 20, 30, 40, 90, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
Hallar:  (A∩ )△B, A△ ( ∩B)Cc Cc
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 30, 50, 55, 60}
= {5, 10, 15, 20, 30, 40, 45, 50, 55, 60}
= {5, 15, 20, 30, 35, 40, 45, 50, 55, 60}
Hallar:  (B∪A)△C, B∩ (A∩C)
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {12, 18, 21, 33, 36}
= {9, 18, 21, 24, 27, 36}
= {6, 9, 12, 15, 21, 36}
Hallar:  (C∪ ) ∩B, C∩ ( ∪B)Ac Ac
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 18, 27, 36, 45, 72, 90}
= {18, 27, 36, 45, 54, 63, 81, 90}
= {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
Hallar:  (B∩ ) − , B△ ( ∪ )C
c Ac Cc Ac
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 7, 11, 17, 19, 23, 29, 31}
= {2, 3, 17, 19, 37}
= {2, 3, 5, 13, 17, 19, 23, 29, 31, 37}
Hallar:  ( ∪ ) ∪ , ∪ ( − )C
c Bc Ac Cc Bc Ac
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 48, 84, 96, 108}
= {12, 24, 60, 84, 120}
= {24, 36, 48, 60, 84, 96, 108, 120}
Hallar:  ( − ) ∩ , ∪ ( ∩ )Ac Bc Cc Ac Bc Cc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 80, 90}
= {20, 50, 70, 80, 100}
= {10, 40, 50, 70, 100}
Hallar:  (C− ) ∪ , C∪ ( − )Bc Ac Bc Ac
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {18, 27, 36, 45, 63, 72, 81, 90}
= {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
= {9, 18, 27, 45, 54, 63, 81}
Hallar:  (C− ) ∩B, C− ( △B)Ac Ac
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {4, 6, 8, 10, 14, 16, 20, 22, 24}
= {2, 6, 10, 12, 16, 22, 24}
= {2, 4, 8, 10, 12, 14, 16, 18, 20, 22}
Hallar:  ( ∩B) − , △ (B− )Ac Cc Ac Cc
21). Dado el conjunto universal:
y los subconjuntos:
22). Dado el conjunto universal:
y los subconjuntos:
23). Dado el conjunto universal:
y los subconjuntos:
24). Dado el conjunto universal:
y los subconjuntos:
25). Dado el conjunto universal:
y los subconjuntos:
26). Dado el conjunto universal:
y los subconjuntos:
27). Dado el conjunto universal:
y los subconjuntos:
28). Dado el conjunto universal:
y los subconjuntos:
29). Dado el conjunto universal:
y los subconjuntos:
30). Dado el conjunto universal:
y los subconjuntos:
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {a, b, e, j, k}
= {e, f , g, h, i, k, l}
= {a, b, c, d, e, f , g, h, i, j, k, l}
Hallar:  ( ∩C) ∪ , ∩ (C− )Ac Bc Ac Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 8, 16, 28, 36, 44}
= {8, 12, 16, 20, 24, 28, 48}
= {4, 8, 12, 16, 20, 28, 32, 40, 44}
Hallar:  ( ∪ ) ∪ , ∩ ( △ )Cc Bc Ac Cc Bc Ac
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 4, 6, 8, 14, 16, 18, 20, 22, 24}
= {2, 4, 6, 12, 14, 16, 18, 22, 24}
= {10, 12, 14, 18, 24}
Hallar:  (A∪ ) ∩B, A△ ( −B)Cc Cc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {8, 16, 24, 36, 40, 48}
= {4, 8, 12, 16, 24, 28, 32, 36, 40, 44, 48}
= {4, 8, 12, 16, 20, 24, 32, 36, 40, 44, 48}
Hallar:  (C∪ ) − , C∩ ( ∩ )Ac Bc Ac Bc
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
= {10, 15, 25, 30, 35, 40, 45, 50, 55, 60}
= {10, 25, 40, 50, 55, 60}
Hallar:  (A△C) ∪B, A∪ (C−B)
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 60, 80, 90}
= {10, 20, 30, 40, 50, 60, 70, 80, 90}
= {10, 20, 30, 50, 60, 70}
Hallar:  (B△ ) ∪C, B∪ ( −C)A
c Ac
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 55, 66, 88, 110}
= {11, 33, 44, 55, 77, 88, 99}
= {22, 44, 66, 88, 99}
Hallar:  (B−C) ∪ , B△ (C△ )Ac Ac
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 4, 6, 10, 12, 14, 16, 18, 20, 22}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
= {4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Hallar:  (A∩B) ∪C, A− (B∩C)
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {a, b, c, d, e, f , h, i, j, l}
= {a, c, f , h, i, l}
= {a, b, e, g, h, i, j, k}
Hallar:  ( − )△ , − ( ∩ )Bc Cc Ac Bc Cc Ac
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 30, 40, 50, 60, 80, 90, 100}
= {10, 40, 50, 60, 90, 100}
Hallar:  (A△ ) ∩B, A△ ( ∪B)Cc Cc
31). Dado el conjunto universal:
y los subconjuntos:
32). Dado el conjunto universal:
y los subconjuntos:
33). Dado el conjunto universal:
y los subconjuntos:
34). Dado el conjunto universal:
y los subconjuntos:
35). Dado el conjunto universal:
y los subconjuntos:
36). Dado el conjunto universal:
y los subconjuntos:
37). Dado el conjunto universal:
y los subconjuntos:
38).Dado el conjunto universal:
y los subconjuntos:
39). Dado el conjunto universal:
y los subconjuntos:
40). Dado el conjunto universal:
y los subconjuntos:
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 6, 8, 12, 16, 18, 20, 22, 24}
= {2, 4, 8, 12, 14, 16, 18, 20}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Hallar:  (B∪ ) ∩C, B∪ ( ∩C)Ac Ac
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {24, 60, 72, 84, 96, 108}
= {12, 24, 36, 72, 84, 108}
= {24, 36, 48, 60, 72, 84, 96, 108, 120}
Hallar:  (C∪B)△ , C△ (B△ )Ac Ac
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 9, 12, 15, 18, 21, 27}
= {18, 21, 27, 30, 33, 36}
= {3, 12, 18, 21, 27, 30, 36}
Hallar:  (B∪C) ∩A, B− (C△A)
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {3, 5, 11, 13, 23}
= {3, 5, 7, 11, 19, 29, 37}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
Hallar:  (C∩A) ∩B, C△ (A△B)
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, o, p, q, r, s, t, u, v, w, x}
= {n, o, p, q, r, s, t, u, v, w}
= {m, n, o, p, q, r, s, t, u, v, w, x}
Hallar:  (B∪A) ∪C, B△ (A∩C)
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 18, 36, 45, 54, 72, 81, 90}
= {9, 18, 27, 45, 81}
= {18, 27, 54, 81, 90}
Hallar:  ( ∩B) ∪ , △ (B∪ )A
c Cc Ac Cc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 12, 16, 20, 28, 32, 48}
= {12, 16, 28, 32, 36, 48}
= {12, 16, 28, 40, 44}
Hallar:  ( ∩C)△ , ∪ (C△ )Ac Bc Ac Bc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 44, 66, 77, 88, 99, 110}
= {11, 44, 55, 77, 99, 110}
= {22, 55, 66, 77, 99}
Hallar:  ( △C)△B, − (C△B)Ac Ac
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 18, 27, 36, 45, 63, 72, 90}
= {9, 18, 27, 36, 45, 54, 72, 81, 90}
= {9, 27, 45, 54, 63, 72, 81}
Hallar:  (B−C) − , B△ (C∪ )Ac Ac
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {20, 40, 80, 90, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
Hallar:  (B∪A) − , B△ (A− )Cc Cc
41). Dado el conjunto universal:
y los subconjuntos:
42). Dado el conjunto universal:
y los subconjuntos:
43). Dado el conjunto universal:
y los subconjuntos:
44). Dado el conjunto universal:
y los subconjuntos:
45). Dado el conjunto universal:
y los subconjuntos:
46). Dado el conjunto universal:
y los subconjuntos:
47). Dado el conjunto universal:
y los subconjuntos:
48). Dado el conjunto universal:
y los subconjuntos:
49). Dado el conjunto universal:
y los subconjuntos:
50). Dado el conjunto universal:
y los subconjuntos:
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, o, p, q, r, s, t, u, v, w, x}
= {n, p, q, r, s}
= {m, n, o, p, r, s, t, w, x}
Hallar:  ( ∩ ) ∪ , ∪ ( − )Ac Cc Bc Ac Cc Bc
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {20, 25, 45, 55, 60}
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50}
= {10, 15, 20, 25, 30, 35, 45, 55, 60}
Hallar:  (A∪ ) ∪ , A∩ ( △ )Bc Cc Bc Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 9, 12, 15, 21, 24, 27, 30, 33, 36}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
= {15, 21, 24, 27, 30}
Hallar:  ( ∪ ) ∪B, ∩ ( −B)Ac Cc Ac Cc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 24, 36, 48, 60, 72, 84, 96, 108}
= {12, 24, 48, 60, 72, 96, 120}
Hallar:  ( △C) −A, − (C∩A)Bc Bc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {24, 36, 60, 72, 96, 108, 120}
= {12, 24, 48, 60, 72, 84, 96, 108, 120}
= {24, 36, 72, 96, 120}
Hallar:  ( −B) −A, − (B∩A)C
c Cc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 32, 40, 56, 80, 88, 96}
= {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 96}
= {8, 32, 40, 48, 80, 88, 96}
Hallar:  (B−C)△ , B△ (C∪ )A
c Ac
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 36, 60, 72, 96}
= {12, 24, 36, 48, 60, 72, 84, 96, 120}
= {12, 48, 60, 72, 84, 108, 120}
Hallar:  ( △B) −A, ∪ (B△A)Cc Cc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 44, 55, 66, 77, 88, 110}
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
= {11, 22, 55, 66, 77, 88, 99, 110}
Hallar:  ( △ ) − , ∩ ( − )Bc Cc Ac Bc Cc Ac
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {a, c, g, h, j, k}
= {a, b, d, f , h, i, k}
= {a, d, f , g, h, i, j, k, l}
Hallar:  ( − ) ∪B, ∩ ( ∪B)Ac Cc Ac Cc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 77, 88, 99, 110}
= {22, 33, 44, 55, 66, 77, 88, 110}
= {11, 22, 33, 44, 77, 88, 99, 110}
Hallar:  (C△A) −B, C∩ (A△B)
51). Dado el conjunto universal:
y los subconjuntos:
52). Dado el conjunto universal:
y los subconjuntos:
53). Dado el conjunto universal:
y los subconjuntos:
54). Dado el conjunto universal:
y los subconjuntos:
55). Dado el conjunto universal:
y los subconjuntos:
56). Dado el conjunto universal:
y los subconjuntos:
57). Dado el conjunto universal:
y los subconjuntos:
58). Dado el conjunto universal:
y los subconjuntos:
59). Dado el conjunto universal:
y los subconjuntos:
60). Dado el conjunto universal:
y los subconjuntos:
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
= {11, 22, 55, 77, 110}
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
Hallar:  (B△ ) ∩ , B− ( ∩ )Ac Cc Ac Cc
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 28, 42, 70, 77}
= {7, 14, 21, 35, 42, 49, 56, 63, 70, 77, 84}
= {28, 42, 70, 77, 84}
Hallar:  (A△ ) − , A− ( − )Bc Cc Bc Cc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 60, 72, 96, 108, 120}
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 36, 48, 60, 72, 108, 120}
Hallar:  (B−A) − , B∩ (A∪ )Cc Cc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 5, 7, 11, 13, 17, 19, 29, 31, 37}
= {2, 3, 5, 7, 11, 13, 19, 23, 29, 31, 37}
= {3, 5, 7, 11, 13, 19, 23, 29, 31}
Hallar:  ( △C) ∩A, ∩ (C△A)Bc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 8, 12, 20, 24, 36, 40, 44, 48}
= {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
= {4, 12, 16, 20, 24, 28, 32, 36, 40}
Hallar:  ( −C) ∩ , ∩ (C△ )A
c Bc Ac Bc
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, o, p, q, r, s, u, x}
= {m, n, o, p, q, r, s, t, u, v, w, x}
= {n, o, p, r, v}
Hallar:  ( △ ) − , ∩ ( △ )C
c Ac Bc Cc Ac Bc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 32, 40, 48, 56, 64, 80, 88, 96}
= {8, 24, 32, 64, 80, 96}
= {16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
Hallar:  (B∪ ) ∩A, B∩ ( ∪A)Cc Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 18, 21, 24, 30, 33, 36}
= {3, 6, 9, 12, 18, 21, 30, 33, 36}
= {6, 15, 18, 21, 24, 27, 30, 36}
Hallar:  (A∪ ) − , A△ ( ∪ )Bc Cc Bc Cc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 8, 12, 20, 24, 28, 36, 40, 44, 48}
= {4, 8, 16, 20, 24, 28, 32, 36, 44, 48}
= {4, 8, 12, 16, 20, 24, 32, 36, 40, 44, 48}
Hallar:  (A△C)△B, A∪ (C−B)
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 16, 20, 24, 28, 32, 40, 44, 48}
= {4, 8, 12, 16, 20, 24, 28, 36, 44, 48}
= {8, 20, 24, 28, 48}
Hallar:  ( △ ) − , ∩ ( △ )Bc Cc Ac Bc Cc Ac
61). Dado el conjunto universal:
y los subconjuntos:
62). Dado el conjunto universal:
y los subconjuntos:
63). Dado el conjunto universal:
y los subconjuntos:
64). Dado el conjunto universal:
y los subconjuntos:
65). Dado el conjunto universal:
y los subconjuntos:
66). Dado el conjunto universal:
y los subconjuntos:
67). Dado el conjunto universal:
y los subconjuntos:
68). Dado el conjunto universal:
y los subconjuntos:
69). Dado el conjunto universal:
y los subconjuntos:
70). Dado el conjunto universal:
y los subconjuntos:
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 32, 40, 48, 64, 72, 80, 96}
= {8, 16, 40, 48, 72, 80, 88, 96}
= {8, 16, 40, 80, 88, 96}
Hallar:  (C−B) ∩A, C∩ (B∩A)
U = {2, 4, 6, 8, 10, 12, 14,16, 18, 20, 22, 24}
A
B
C
= {2, 4, 6, 8, 10, 12, 14, 16, 22, 24}
= {4, 6, 8, 10, 14, 16}
= {10, 12, 18, 20, 22, 24}
Hallar:  (B−A) ∩C, B△ (A−C)
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 4, 14, 22, 24}
= {4, 6, 8, 10, 12, 20, 22, 24}
= {2, 6, 8, 14, 16, 24}
Hallar:  ( △ ) ∩C, ∪ ( ∪C)Ac Bc Ac Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 12, 16, 24, 28, 32, 48}
= {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
= {4, 12, 28, 36, 40, 44}
Hallar:  ( ∩A) ∩B, − (A∪B)Cc Cc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 90}
= {20, 30, 60, 80, 90, 100}
Hallar:  (A∩B) −C, A△ (B△C)
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 21, 28, 35, 42, 56, 63, 77}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 21, 42, 49, 56, 70, 77}
Hallar:  ( ∩ )△ , ∪ ( − )A
c Bc Cc Ac Bc Cc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {12, 24, 30, 36, 42, 54, 60}
= {6, 12, 18, 30, 36, 48, 54, 60, 66, 72}
= {12, 18, 24, 36, 48, 54, 66}
Hallar:  (A△ ) −B, A∩ ( −B)Cc Cc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 60, 72, 84, 96, 120}
= {12, 24, 36, 48, 60, 72, 84, 96, 120}
= {12, 24, 36, 60, 72, 84, 96, 108, 120}
Hallar:  ( △A)△ , ∪ (A△ )Cc Bc Cc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 8, 12, 16, 20, 28, 32, 36, 40, 44, 48}
= {12, 16, 20, 24, 32, 40, 48}
= {4, 8, 12, 20, 24, 28, 32, 48}
Hallar:  ( ∩B) ∪C, − (B△C)Ac Ac
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {a, b, c, d, e, g, i, j, k, l}
= {a, b, c, d, e, f , g, i, j, k, l}
= {a, c, d, e, f , g, i, j, k, l}
Hallar:  (C△ ) − , C△ ( ∪ )Bc Ac Bc Ac
71). Dado el conjunto universal:
y los subconjuntos:
72). Dado el conjunto universal:
y los subconjuntos:
73). Dado el conjunto universal:
y los subconjuntos:
74). Dado el conjunto universal:
y los subconjuntos:
75). Dado el conjunto universal:
y los subconjuntos:
76). Dado el conjunto universal:
y los subconjuntos:
77). Dado el conjunto universal:
y los subconjuntos:
78). Dado el conjunto universal:
y los subconjuntos:
79). Dado el conjunto universal:
y los subconjuntos:
80). Dado el conjunto universal:
y los subconjuntos:
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {b, c, d, e, f , g, i, j, k, l}
= {b, d, e, g, l}
= {b, c, d, e, f , h, j, k, l}
Hallar:  (C−B) ∩A, C∪ (B△A)
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {4, 6, 8, 10, 14, 16, 18, 20, 22, 24}
= {4, 6, 10, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 6, 8, 10, 12, 18, 20, 22, 24}
Hallar:  (B∩A) ∩ , B△ (A− )Cc Cc
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {21, 35, 42, 63, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 77, 84}
= {14, 21, 28, 42, 49, 56, 63, 70, 77, 84}
Hallar:  (A− ) ∪ , A△ ( ∩ )Cc Bc Cc Bc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {30, 40, 50, 70, 80, 90, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 20, 40, 50, 60, 70, 80, 90, 100}
Hallar:  ( −C) − , − (C∩ )Bc Ac Bc Ac
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 8, 12, 16, 20, 24, 28, 32, 36, 44, 48}
= {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
= {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
Hallar:  (B∩A) ∩ , B∩ (A∩ )C
c Cc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
= {12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
= {6, 12, 18, 24, 30, 54, 72}
Hallar:  (A△ )△ , A∩ ( − )Bc C
c Bc Cc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 24, 32, 40, 48, 56, 80, 88, 96}
= {8, 24, 32, 40, 48, 56, 64, 72, 80, 88}
= {8, 24, 40, 48, 64, 80, 96}
Hallar:  ( ∪ )△ , − ( ∪ )Ac Bc Cc Ac Bc Cc
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, o, p, s, u, v, x}
= {m, n, p, q, t, u, w, x}
= {n, o, p, r, s, t, x}
Hallar:  (B△A)△C, B△ (A∩C)
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {14, 28, 35, 42, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
Hallar:  (B∩C) ∩A, B∪ (C∪A)
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 12, 15, 21, 33}
= {6, 9, 15, 18, 21, 24, 27}
= {6, 9, 15, 21, 24, 30, 33, 36}
Hallar:  ( △C) ∪B, ∩ (C−B)Ac Ac
81). Dado el conjunto universal:
y los subconjuntos:
82). Dado el conjunto universal:
y los subconjuntos:
83). Dado el conjunto universal:
y los subconjuntos:
84). Dado el conjunto universal:
y los subconjuntos:
85). Dado el conjunto universal:
y los subconjuntos:
86). Dado el conjunto universal:
y los subconjuntos:
87). Dado el conjunto universal:
y los subconjuntos:
88). Dado el conjunto universal:
y los subconjuntos:
89). Dado el conjunto universal:
y los subconjuntos:
90). Dado el conjunto universal:
y los subconjuntos:
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 8, 10, 12, 20, 22, 24}
= {2, 4, 8, 14, 18, 20, 22, 24}
= {2, 6, 10, 14, 16, 20, 22, 24}
Hallar:  (B△ ) ∪C, B− ( ∪C)Ac Ac
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {18, 24, 36, 54, 60, 72}
= {12, 24, 30, 36, 42, 54, 60, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 72}
Hallar:  ( ∪ ) ∪A, ∪ ( ∪A)Cc Bc Cc Bc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {18, 24, 30, 36, 48, 54, 72}
= {12, 24, 30, 36, 42, 48, 54, 60, 66, 72}
= {6, 12, 18, 24, 30, 42, 48, 60}
Hallar:  (A△ ) −B, A∩ ( ∩B)Cc Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {12, 15, 21, 24, 27, 30, 36}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
Hallar:  ( ∩B) ∩A, ∪ (B△A)Cc Cc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 7, 19}
= {2, 3, 5, 13, 29, 37}
= {2, 5, 7, 13, 17, 23, 29, 31, 37}
Hallar:  (C− ) ∩B, C△ ( ∩B)A
c Ac
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 21, 28, 35, 42, 49, 56, 77, 84}
= {7, 14, 28, 35, 42, 49, 56, 63, 84}
= {21, 28, 35, 63, 77, 84}
Hallar:  ( ∩B) − , ∩ (B− )C
c Ac Cc Ac
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 50, 60, 70, 90, 100}
= {40, 50, 70, 80, 100}
= {10, 20, 30, 70, 80, 90}
Hallar:  (B∩C) −A, B△ (C−A)
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 44, 55, 66, 88, 99, 110}
= {11, 33, 44, 55, 66, 77, 88, 99, 110}
= {11, 22, 33, 55, 66, 77, 99, 110}
Hallar:  (C∩A) ∪B, C∪ (A△B)
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {18, 36, 45, 54, 63, 72, 81, 90}
= {9, 18, 27, 45, 54, 63, 72, 81, 90}
= {9, 18, 27, 45, 72, 90}
Hallar:  ( ∪ ) ∪A, ∪ ( △A)Cc Bc Cc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
= {4, 8, 20, 32, 36}
= {4, 8, 12, 20, 28, 32, 36, 44}
Hallar:  (A△ ) ∩C, A− ( ∩C)Bc Bc
91). Dado el conjunto universal:
y los subconjuntos:
92). Dado el conjunto universal:
y los subconjuntos:
93). Dado el conjunto universal:
y los subconjuntos:
94). Dado el conjunto universal:
y los subconjuntos:
95). Dado el conjunto universal:
y los subconjuntos:
96). Dado el conjunto universal:
y los subconjuntos:
97). Dado el conjunto universal:
y los subconjuntos:
98). Dado el conjunto universal:
y los subconjuntos:
99). Dado el conjunto universal:
y los subconjuntos:
100). Dado el conjunto universal:
y los subconjuntos:
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {12, 18, 24, 42, 48, 54, 60, 72}
= {18, 30, 36, 42, 48, 54, 60, 66, 72}
= {6, 24, 30, 36, 42, 48, 54, 60, 72}
Hallar:  ( △ ) − , − ( △ )Ac Bc Cc Ac Bc Cc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 24, 36, 48, 60, 96}
= {36, 48, 60, 72, 84, 96, 108}
Hallar:  ( ∪B)△ , ∪ (B∩ )Ac Cc Ac Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 9, 15, 18, 21, 27, 30, 33, 36}
= {3, 6, 9, 15,18, 21, 24, 27, 30, 33, 36}
= {3, 6, 9, 12, 18, 21, 24, 27, 30, 33, 36}
Hallar:  ( △ ) ∩ , ∪ ( △ )Cc Ac Bc Cc Ac Bc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {6, 8, 10, 14, 24}
= {2, 4, 6, 8, 10, 14, 18}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Hallar:  (A△ ) ∪B, A− ( ∩B)Cc Cc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 32, 40, 64, 72, 80, 88, 96}
= {8, 16, 24, 48, 56, 64, 72, 80, 96}
= {8, 16, 40, 48, 56, 64, 80, 88, 96}
Hallar:  (C− ) ∪B, C− ( ∪B)A
c Ac
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {18, 27, 36, 45, 54, 63, 72, 81}
= {9, 18, 27, 36, 45, 63, 72, 90}
= {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
Hallar:  ( −B) − , ∩ (B△ )C
c Ac Cc Ac
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, o, r, s, t, u}
= {n, o, p, q, s, w, x}
= {m, n, o, p, q, r, s, t, u, v, w, x}
Hallar:  ( −A) −B, △ (A−B)Cc Cc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 72}
Hallar:  ( ∪B) − , ∩ (B∩ )Cc Ac Cc Ac
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 60, 72, 84, 108, 120}
= {36, 60, 72, 84, 96}
= {12, 24, 36, 48, 72, 96, 120}
Hallar:  ( −C) − , ∩ (C− )Bc Ac Bc Ac
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, o, p, q, r, s, t, u, v, x}
= {m, o, p, q, r, s, t, u, v, w, x}
= {m, n, o, q, r, t, u, v, w, x}
Hallar:  (B∩A) ∪C, B∩ (A△C)
101). Dado el conjunto universal:
y los subconjuntos:
102). Dado el conjunto universal:
y los subconjuntos:
103). Dado el conjunto universal:
y los subconjuntos:
104). Dado el conjunto universal:
y los subconjuntos:
105). Dado el conjunto universal:
y los subconjuntos:
106). Dado el conjunto universal:
y los subconjuntos:
107). Dado el conjunto universal:
y los subconjuntos:
108). Dado el conjunto universal:
y los subconjuntos:
109). Dado el conjunto universal:
y los subconjuntos:
110). Dado el conjunto universal:
y los subconjuntos:
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {12, 24, 30, 36, 60, 72}
= {6, 12, 42, 48, 60, 66}
= {6, 12, 36, 42, 48, 54, 60, 66}
Hallar:  ( ∩ ) − , ∪ ( ∩ )Cc Bc Ac Cc Bc Ac
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 18, 27, 36, 54, 63, 72, 81, 90}
= {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
= {9, 18, 45, 54, 81, 90}
Hallar:  (B∪ ) −C, B∩ ( ∩C)Ac Ac
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 10, 20, 25, 30, 35, 40, 45, 50, 55}
= {10, 15, 20, 35, 45, 60}
= {5, 15, 20, 30, 40, 50}
Hallar:  (B△C)△ , B∩ (C△ )Ac Ac
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 24, 42, 48, 54, 66, 72}
= {24, 30, 42, 48, 66, 72}
= {12, 18, 24, 30, 36, 48, 66}
Hallar:  (A△ ) −B, A△ ( ∩B)Cc Cc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 32, 40, 56, 64, 72, 80, 96}
= {16, 24, 32, 48, 96}
= {24, 32, 48, 64, 72, 80}
Hallar:  (C− ) ∩A, C∪ ( −A)Bc Bc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 32, 40, 64, 88}
= {40, 48, 56, 80, 88}
= {16, 24, 32, 64, 80, 96}
Hallar:  ( − ) −A, ∪ ( ∩A)C
c Bc Cc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {8, 12, 16, 20, 24, 28, 32, 36, 40, 48}
= {8, 16, 24, 32, 36, 40, 44, 48}
= {8, 12, 20, 24, 28, 32, 36, 40, 44, 48}
Hallar:  ( △B) − , △ (B△ )Ac Cc Ac Cc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 18, 24, 30, 36, 42, 54, 66, 72}
= {6, 12, 18, 24, 30, 42, 48, 54, 60, 72}
= {12, 24, 30, 36, 42, 48, 54, 60, 66, 72}
Hallar:  ( −A) ∪B, ∩ (A−B)Cc Cc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 40, 50, 60, 70, 90, 100}
= {10, 30, 60, 70, 80, 90}
= {10, 40, 60, 90, 100}
Hallar:  (B∪ ) ∩A, B− ( −A)Cc Cc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
= {16, 24, 32, 48, 64, 88, 96}
= {8, 32, 40, 72, 88, 96}
Hallar:  ( − ) ∩ , ∩ ( − )Cc Ac Bc Cc Ac Bc
111). Dado el conjunto universal:
y los subconjuntos:
112). Dado el conjunto universal:
y los subconjuntos:
113). Dado el conjunto universal:
y los subconjuntos:
114). Dado el conjunto universal:
y los subconjuntos:
115). Dado el conjunto universal:
y los subconjuntos:
116). Dado el conjunto universal:
y los subconjuntos:
117). Dado el conjunto universal:
y los subconjuntos:
118). Dado el conjunto universal:
y los subconjuntos:
119). Dado el conjunto universal:
y los subconjuntos:
120). Dado el conjunto universal:
y los subconjuntos:
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 36, 84, 96, 108}
= {24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 24, 48, 60, 72, 84, 96, 108, 120}
Hallar:  (B∪ )△A, B△ ( △A)Cc Cc
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 15, 20, 25, 30, 45, 55}
= {5, 15, 20, 25, 35, 40, 45, 50, 60}
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
Hallar:  ( ∪ ) −A, ∪ ( ∪A)Cc Bc Cc Bc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 20, 40, 50, 70, 80, 100}
= {30, 40, 50, 60, 70, 80, 90, 100}
Hallar:  (C− ) ∪ , C− ( ∪ )Bc Ac Bc Ac
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 5, 7, 11, 13, 17, 19, 29, 31, 37}
= {2, 3, 7, 13, 17, 19, 23, 29, 37}
= {2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37}
Hallar:  (C∪A) ∩ , C△ (A∩ )Bc Bc
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, p, r, u, v}
= {m, n, o, p, q, r, s, t, u, v, w, x}
= {m, n, o, p, q, r, s, t, u, v}
Hallar:  ( △ ) ∩C, ∩ ( ∩C)A
c Bc Ac Bc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 84, 96}
= {12, 24, 60, 72, 84, 96, 108}
= {24, 36, 48, 60, 72, 84, 108, 120}
Hallar:  ( △ ) ∩A, ∪ ( −A)Bc C
c Bc Cc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
= {16, 24, 32, 48, 64, 72, 88, 96}
= {8, 16, 40, 64, 72, 80}
Hallar:  ( △ ) −C, ∪ ( ∩C)Bc Ac Bc Ac
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 24, 48, 60, 72, 84, 96, 108, 120}
= {12, 24, 36, 48, 84, 96, 108, 120}
Hallar:  (C△B) ∪A, C∩ (B∪A)
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {6, 9, 18, 21, 27, 33, 36}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 36}
= {6, 9, 12, 18, 24, 30}
Hallar:  ( ∪ ) ∩A, △ ( ∩A)Cc Bc Cc Bc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 18, 72, 81, 90}
= {9, 27, 36, 45, 54, 63, 72, 81, 90}
= {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
Hallar:  ( −B) −A, − (B△A)Cc Cc
121). Dado el conjunto universal:
y los subconjuntos:
122). Dado el conjunto universal:
y los subconjuntos:
123). Dado el conjunto universal:
y los subconjuntos:
124). Dado el conjunto universal:
y los subconjuntos:
125). Dado el conjunto universal:
y los subconjuntos:
126). Dado el conjunto universal:
y los subconjuntos:
127). Dado el conjunto universal:
y los subconjuntos:
128). Dado el conjunto universal:
y los subconjuntos:
129). Dado el conjunto universal:
y los subconjuntos:
130). Dado el conjunto universal:
y los subconjuntos:
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {8, 16, 20, 24, 28, 48}
= {8, 12, 28, 40, 44}
= {8, 16, 20, 24, 28, 32, 40, 44, 48}
Hallar:  ( △ ) − , △ ( − )Bc Cc Ac Bc Cc Ac
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 12, 15, 18, 24, 33, 36}
= {12, 18, 21, 30, 33, 36}
= {9, 12, 15, 18, 21, 24, 27, 33, 36}
Hallar:  (C△B) −A, C∩ (B−A)
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 90}
= {10, 20, 40, 70, 100}
Hallar:  ( −B) ∪A, △ (B∪A)Cc Cc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 7, 11, 13, 17, 19, 23, 31}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 3, 5, 7, 11, 17, 19, 23, 29, 31, 37}
Hallar:  ( △ )△ , ∪ ( ∩ )CcAc Bc Cc Ac Bc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {20, 30, 40, 50, 60, 80, 90, 100}
= {10, 20, 60, 90, 100}
= {10, 20, 40, 50, 60, 80, 100}
Hallar:  ( ∪ ) − , − ( − )C
c Ac Bc Cc Ac Bc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 18, 24, 30, 36, 42, 48, 60}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
= {6, 12, 18, 24, 36, 42, 48, 54, 60, 66, 72}
Hallar:  ( △C)△ , ∪ (C∪ )A
c Bc Ac Bc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 36, 48, 60, 72, 96, 108}
= {12, 24, 36, 60, 72, 84, 96, 108, 120}
= {12, 24, 36, 48, 84, 96, 108, 120}
Hallar:  (B∪A) ∪C, B∪ (A−C)
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 9, 12, 21, 27, 30, 33}
= {3, 6, 12, 15, 21, 24, 27, 30, 36}
= {3, 9, 12, 18, 21, 24, 27, 30, 33}
Hallar:  ( ∩A)△C, △ (A−C)Bc Bc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {6, 8, 16, 18, 20, 22, 24}
= {2, 4, 6, 16, 18, 20, 22, 24}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Hallar:  (A∩ ) ∪ , A∩ ( − )Cc Bc Cc Bc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 44, 66, 99}
= {11, 22, 33, 44, 55, 99, 110}
= {11, 22, 33, 44, 55, 66, 88, 110}
Hallar:  (C∩A) −B, C∩ (A△B)
131). Dado el conjunto universal:
y los subconjuntos:
132). Dado el conjunto universal:
y los subconjuntos:
133). Dado el conjunto universal:
y los subconjuntos:
134). Dado el conjunto universal:
y los subconjuntos:
135). Dado el conjunto universal:
y los subconjuntos:
136). Dado el conjunto universal:
y los subconjuntos:
137). Dado el conjunto universal:
y los subconjuntos:
138). Dado el conjunto universal:
y los subconjuntos:
139). Dado el conjunto universal:
y los subconjuntos:
140). Dado el conjunto universal:
y los subconjuntos:
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
= {22, 33, 55, 77, 88}
= {11, 33, 44, 55, 66, 77, 99, 110}
Hallar:  (A∩C)△ , A∩ (C△ )Bc Bc
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {n, o, p, q, r, s, u, v}
= {n, o, p, q, r, s, t, v, w}
= {m, n, o, p, q, r, s, t, u, w}
Hallar:  (A−B) −C, A− (B△C)
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {12, 24, 30, 36, 42, 60, 72}
= {6, 12, 18, 24, 36, 42, 48, 54, 60, 66, 72}
= {12, 18, 24, 30, 36, 42, 54, 72}
Hallar:  (B−C)△A, B△ (C△A)
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 7, 11, 17, 19, 29, 37}
= {3, 5, 11, 13, 17, 23, 29, 37}
= {5, 11, 17, 23, 31, 37}
Hallar:  ( ∪ ) − , ∪ ( ∪ )Ac Cc Bc Ac Cc Bc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 36, 42, 60, 66}
= {6, 12, 18, 24, 30, 36, 42, 54, 66, 72}
= {12, 30, 54, 66, 72}
Hallar:  (C△A) −B, C∪ (A−B)
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 15, 20, 25, 30, 40, 45, 55, 60}
= {20, 40, 45, 50, 60}
= {5, 10, 20, 30, 35, 40, 45, 50, 55, 60}
Hallar:  ( ∩A) − , − (A− )Bc C
c Bc Cc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 5, 7, 13, 17, 19, 29}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {5, 7, 13, 17, 23}
Hallar:  ( ∪B)△ , △ (B∪ )Ac Cc Ac Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
= {3, 6, 9, 12, 18, 24, 27, 30, 33, 36}
= {6, 9, 12, 15, 18, 21, 24, 27, 30, 33}
Hallar:  ( −B) ∩C, ∪ (B−C)Ac Ac
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {4, 6, 8, 10, 14, 18}
= {2, 4, 6, 8, 14, 18, 22, 24}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Hallar:  ( ∩C) ∩ , ∪ (C− )Bc Ac Bc Ac
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 4, 8, 10, 14, 20}
= {4, 6, 10, 12, 14, 18, 20, 22, 24}
= {2, 4, 6, 10, 14, 16, 22}
Hallar:  ( − ) ∪ , − ( ∩ )Bc Ac Cc Bc Ac Cc
141). Dado el conjunto universal:
y los subconjuntos:
142). Dado el conjunto universal:
y los subconjuntos:
143). Dado el conjunto universal:
y los subconjuntos:
144). Dado el conjunto universal:
y los subconjuntos:
145). Dado el conjunto universal:
y los subconjuntos:
146). Dado el conjunto universal:
y los subconjuntos:
147). Dado el conjunto universal:
y los subconjuntos:
148). Dado el conjunto universal:
y los subconjuntos:
149). Dado el conjunto universal:
y los subconjuntos:
150). Dado el conjunto universal:
y los subconjuntos:
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 10, 40, 50, 55, 60}
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
= {10, 20, 25, 35, 45}
Hallar:  ( − ) ∪A, ∩ ( −A)Bc Cc Bc Cc
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, o, p, q, r, s, t, v, w, x}
= {m, n, o, q, s, t, u, v, w, x}
= {n, p, q, r, s, t, u, v, w, x}
Hallar:  ( △C) − , ∪ (C− )Ac Bc Ac Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 12, 24, 32, 40, 44}
= {4, 8, 16, 20, 24, 28, 32, 36, 40, 44}
= {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
Hallar:  ( ∩C) ∪ , ∪ (C∪ )Bc Ac Bc Ac
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 6, 8, 10, 14, 16, 20, 24}
= {2, 4, 6, 10, 12, 16, 20, 22}
= {2, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Hallar:  (B△C) ∩A, B△ (C∩A)
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {48, 60, 72, 96, 108, 120}
= {12, 24, 36, 48, 84, 96, 108, 120}
= {12, 24, 36, 48, 60, 96, 108, 120}
Hallar:  (A△B) ∩ , A∩ (B− )C
c Cc
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, o, p, q, r, w, x}
= {m, n, p, q, r, s, t, u, v, w, x}
= {o, q, s, u, x}
Hallar:  (B△C) ∪A, B△ (C−A)
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {o, r, s, w, x}
= {n, o, r, s, t, u, v, w, x}
= {o, q, r, v, x}
Hallar:  ( ∪A) ∪B, ∪ (A−B)Cc Cc
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 10, 15, 20, 25, 35, 55}
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
= {5, 20, 30, 40, 45, 50, 55}
Hallar:  ( ∩A) − , ∩ (A∩ )Bc Cc Bc Cc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 30, 50, 60, 80, 90}
= {10, 20, 30, 40, 50, 60, 70, 80, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 100}
Hallar:  (C∪A) ∪B, C△ (A∩B)
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
= {4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 6, 8, 12, 18, 22}
Hallar:  ( − ) − , − ( △ )Bc Cc Ac Bc Cc Ac
151). Dado el conjunto universal:
y los subconjuntos:
152). Dado el conjunto universal:
y los subconjuntos:
153). Dado el conjunto universal:
y los subconjuntos:
154). Dado el conjunto universal:
y los subconjuntos:
155). Dado el conjunto universal:
y los subconjuntos:
156). Dado el conjunto universal:
y los subconjuntos:
157). Dado el conjunto universal:
y los subconjuntos:
158). Dado el conjunto universal:
y los subconjuntos:
159). Dado el conjunto universal:
y los subconjuntos:
160). Dado el conjunto universal:
y los subconjuntos:
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 11, 13, 29, 31}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 3, 5, 7, 11, 17, 19, 23, 29, 31}
Hallar:  (A− )△C, A∪ ( ∩C)Bc Bc
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 84}
= {14, 21, 28, 35, 49, 56}
= {21, 35, 42, 56, 70, 77, 84}
Hallar:  ( ∪ )△ , − ( △ )Bc Ac Cc Bc Ac Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 9, 12, 15, 18, 21, 27, 30, 33, 36}
= {3, 6, 9, 12, 15, 21, 27, 30, 33, 36}
= {3, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
Hallar:  (A−B) ∩ , A△ (B△ )Cc Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 12, 21, 24, 27, 30}
= {3, 9, 15, 18, 24, 27, 33, 36}
= {3, 6, 12, 15, 18, 21, 24, 30, 36}
Hallar:  (C∩ ) ∩ , C− ( − )Bc Ac Bc Ac
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {14, 28, 42, 49, 63, 77, 84}
= {21, 28, 35, 63, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
Hallar:  ( △ )△B, ∪ ( △B)A
c Cc Ac Cc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 13, 17, 19, 31, 37}
= {2, 3, 5, 7, 11, 13, 17, 19,23, 29, 31, 37}
= {2, 7, 11, 13, 17, 19, 23, 29, 31, 37}
Hallar:  ( − ) −C, △ ( ∩C)Bc A
c Bc Ac
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {d, e, f , i, j, l}
= {a, d, e, f , g, j}
= {a, b, c, d, e, f , g, h, j, k}
Hallar:  (B∩C) − , B△ (C△ )Ac Ac
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 60, 72, 84, 120}
= {24, 36, 60, 72, 96, 120}
= {12, 48, 72, 96, 108}
Hallar:  (A−C) ∪ , A− (C∪ )Bc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 8, 12, 16, 20, 28, 32, 40, 44, 48}
= {4, 16, 20, 24, 28, 32, 36, 40, 44, 48}
= {4, 8, 12, 16, 20, 28, 36, 40, 44}
Hallar:  (A∪C) ∪B, A− (C−B)
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {33, 44, 55, 66, 99}
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
= {22, 33, 44, 77, 88, 99, 110}
Hallar:  (A△ ) ∪ , A− ( ∪ )Cc Bc Cc Bc
161). Dado el conjunto universal:
y los subconjuntos:
162). Dado el conjunto universal:
y los subconjuntos:
163). Dado el conjunto universal:
y los subconjuntos:
164). Dado el conjunto universal:
y los subconjuntos:
165). Dado el conjunto universal:
y los subconjuntos:
166). Dado el conjunto universal:
y los subconjuntos:
167). Dado el conjunto universal:
y los subconjuntos:
168). Dado el conjunto universal:
y los subconjuntos:
169). Dado el conjunto universal:
y los subconjuntos:
170). Dado el conjunto universal:
y los subconjuntos:
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, o, p, s, t, w}
= {m, n, o, p, r, x}
= {r, s, t, u, v}
Hallar:  ( ∪ ) ∩B, − ( △B)Ac Cc Ac Cc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {4, 6, 8, 10, 12, 14, 16, 22, 24}
= {2, 8, 10, 12, 14, 16, 18, 20, 24}
= {8, 10, 12, 14, 16, 20, 24}
Hallar:  (A∩ )△C, A∩ ( −C)Bc Bc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 30, 50, 80, 100}
= {30, 40, 60, 70, 80, 100}
Hallar:  ( ∩ ) ∪ , ∩ ( △ )Cc Ac Bc Cc Ac Bc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {18, 24, 42, 48, 54, 60, 66, 72}
= {24, 48, 60, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
Hallar:  (A∩B) −C, A∩ (B−C)
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 40, 60, 80, 100}
= {10, 20, 30, 60, 70, 90, 100}
= {10, 30, 60, 70, 100}
Hallar:  (B∩A) ∪C, B△ (A△C)
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {p, r, s, v, w, x}
= {m, n, p, v, w}
= {q, r, s, t, u, x}
Hallar:  (B∪ ) − , B− ( ∩ )A
c Cc Ac Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 18, 21, 24, 33}
= {3, 6, 12, 18, 21, 24, 27, 30, 33, 36}
= {3, 6, 12, 15, 24, 36}
Hallar:  ( ∩ ) ∩A, ∩ ( ∪A)Cc Bc Cc Bc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
= {11, 22, 33, 55, 66, 88, 99, 110}
= {11, 22, 33, 44, 66, 77, 110}
Hallar:  (A△B) − , A∩ (B∪ )Cc Cc
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {10, 20, 25, 35, 40, 45, 50, 60}
= {5, 10, 15, 25, 35, 40, 50, 55, 60}
= {5, 10, 15, 20, 25, 30, 40, 50}
Hallar:  ( −C) ∪ , △ (C∩ )Bc Ac Bc Ac
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 5, 7, 17, 19, 23, 29, 37}
= {2, 3, 5, 7, 11, 19, 23, 29, 31, 37}
Hallar:  (A− ) ∪ , A− ( − )Cc Bc Cc Bc
171). Dado el conjunto universal:
y los subconjuntos:
172). Dado el conjunto universal:
y los subconjuntos:
173). Dado el conjunto universal:
y los subconjuntos:
174). Dado el conjunto universal:
y los subconjuntos:
175). Dado el conjunto universal:
y los subconjuntos:
176). Dado el conjunto universal:
y los subconjuntos:
177). Dado el conjunto universal:
y los subconjuntos:
178). Dado el conjunto universal:
y los subconjuntos:
179). Dado el conjunto universal:
y los subconjuntos:
180). Dado el conjunto universal:
y los subconjuntos:
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 60, 84, 96, 108, 120}
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 24, 36, 72, 96, 108}
Hallar:  ( −A) −B, △ (A△B)Cc Cc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 60, 72}
= {12, 24, 36, 48, 96, 108, 120}
= {24, 36, 48, 72, 108, 120}
Hallar:  (C△ ) ∩ , C∩ ( − )Bc Ac Bc Ac
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 77, 99, 110}
= {11, 22, 33, 66, 77, 110}
= {22, 33, 44, 99, 110}
Hallar:  (C∪ ) − , C− ( ∪ )Bc Ac Bc Ac
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 8, 12, 16, 20, 24, 28, 32, 40, 44, 48}
= {4, 8, 12, 16, 20, 24, 36, 40, 44, 48}
= {4, 8, 12, 16, 24, 28, 32, 36, 40, 48}
Hallar:  ( −A) − , − (A∪ )Cc Bc Cc Bc
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {b, d, e, f , h, i}
= {a, b, c, d, e, f , g, i, j}
= {a, b, c, d, e, g, h, j, k, l}
Hallar:  ( ∩B) −A, ∩ (B∪A)C
c Cc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 40, 90, 100}
= {10, 70, 80, 90, 100}
= {20, 30, 50, 80, 90, 100}
Hallar:  (C△ )△A, C− ( △A)Bc Bc
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, r, s, t}
= {p, q, r, u, v, w}
= {m, n, q, r, s, t, u, v, w, x}
Hallar:  (C−B) ∩ , C∩ (B∪ )Ac Ac
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {36, 60, 84, 96, 120}
= {24, 36, 48, 60, 84, 96, 108}
= {12, 36, 48, 72, 84, 108, 120}
Hallar:  ( −B) −C, ∩ (B∪C)Ac Ac
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 27, 36, 45, 54, 72, 81}
= {9, 18, 45, 54, 81, 90}
= {9, 18, 45, 54, 63, 90}
Hallar:  ( ∩ ) − , △ ( ∩ )Ac Bc Cc Ac Bc Cc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 40, 48, 72, 96}
= {16, 24, 32, 40, 48, 56, 80, 96}
= {8, 16, 24, 40, 48, 56, 72, 80, 96}
Hallar:  (A−B)△ , A△ (B− )Cc Cc
181). Dado el conjunto universal:
y los subconjuntos:
182). Dado el conjunto universal:
y los subconjuntos:
183). Dado el conjunto universal:
y los subconjuntos:
184). Dado el conjunto universal:
y los subconjuntos:
185). Dado el conjunto universal:
y los subconjuntos:
186). Dado el conjunto universal:
y los subconjuntos:
187). Dado el conjunto universal:
y los subconjuntos:
188). Dado el conjunto universal:
y los subconjuntos:
189). Dado el conjunto universal:
y los subconjuntos:
190). Dado el conjunto universal:
y los subconjuntos:
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 20, 30, 40, 50, 70, 80, 90, 100}
Hallar:  ( △C) − , − (C∩ )Ac Bc Ac Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {12, 20, 28, 32, 36, 44}
= {8, 24, 32, 36, 40, 48}
= {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
Hallar:  (C∪ ) −B, C∪ ( ∪B)Ac Ac
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 33, 44, 55, 66, 77, 88, 99, 110}
= {22, 33, 44, 55, 66, 77, 88, 99, 110}
= {11, 22, 33, 55, 66, 77, 88, 99, 110}
Hallar:  (B−C) − , B− (C△ )Ac Ac
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {6, 8, 10, 14, 18, 20, 22}
= {2, 4, 6, 10, 12, 14, 16, 18, 20, 22, 24}
= {4, 12, 14, 18, 20, 22}
Hallar:  ( ∩ )△A, △ ( △A)Cc Bc Cc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
= {4, 8, 16, 20, 24, 28, 32, 44, 48}
= {4, 16, 20, 28, 32, 36, 44}
Hallar:  (A∩ ) ∪C, A∪ ( △C)Bc Bc
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, o, s, t, u, v, w}
= {m, n, o, p, q, r, s, t, u, w, x}
= {m, n, p, s, t, u, v, x}
Hallar:  ( −C) ∩ , ∩ (C∩ )A
c Bc Ac Bc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {8, 10, 14, 18, 22, 24}
= {2, 4, 6, 8, 10, 12, 14, 18, 20, 24}
= {2, 10, 12, 14, 22, 24}
Hallar:  (C∩ )△A, C− ( △A)Bc Bc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24}
= {8, 10, 14, 16, 22, 24}
= {12, 14, 16, 18, 20, 22, 24}
Hallar:  ( △ )△B, △ ( △B)Cc Ac Cc Ac
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 42, 56, 63, 84}
= {7, 14, 35, 42, 49, 56,77, 84}
= {7, 14, 49, 56, 63, 70, 77, 84}
Hallar:  (A∪B) ∪C, A∩ (B∩C)
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
= {33, 55, 66, 88, 99, 110}
= {11, 33, 66, 77, 88, 99, 110}
Hallar:  (B∪ )△C, B∩ ( ∪C)Ac Ac
191). Dado el conjunto universal:
y los subconjuntos:
192). Dado el conjunto universal:
y los subconjuntos:
193). Dado el conjunto universal:
y los subconjuntos:
194). Dado el conjunto universal:
y los subconjuntos:
195). Dado el conjunto universal:
y los subconjuntos:
196). Dado el conjunto universal:
y los subconjuntos:
197). Dado el conjunto universal:
y los subconjuntos:
198). Dado el conjunto universal:
y los subconjuntos:
199). Dado el conjunto universal:
y los subconjuntos:
200). Dado el conjunto universal:
y los subconjuntos:
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 44, 55, 66, 88, 99, 110}
= {11, 33, 44, 55, 66, 77, 88, 99, 110}
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
Hallar:  (B∩A) ∩C, B∩ (A△C)
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
= {9, 18, 36, 45, 54, 63, 72}
= {18, 27, 54, 63, 81, 90}
Hallar:  ( ∪C) ∪ , − (C△ )Bc Ac Bc Ac
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {a, b, c, d, e, f , g, i, k, l}
= {a, b, c, d, e, f , g, h, i, j, k, l}
= {a, b, d, g, h, i, k}
Hallar:  ( ∩C) ∩B, ∪ (C−B)Ac Ac
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 48, 60, 72, 96, 108, 120}
= {12, 24, 48, 60, 72, 84, 96, 108}
= {12, 24, 36, 48, 72, 96, 120}
Hallar:  (C△B) −A, C△ (B△A)
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 44, 55, 66, 77, 88, 99}
= {22, 33, 66, 77, 88, 99, 110}
= {33, 44, 55, 66, 77, 88, 110}
Hallar:  ( △ )△B, ∩ ( ∩B)C
c Ac Cc Ac
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 32, 40, 48, 56, 72, 80, 88, 96}
= {8, 16, 24, 32, 40, 56, 64, 72, 80, 88, 96}
= {8, 24, 40, 48, 56, 64, 72, 80}
Hallar:  (C∩A) −B, C∩ (A△B)
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {a, c, d, e, f , g, h, i, j, k, l}
= {a, d, f , g, h, i, j, k, l}
= {b, c, d, f , g, h, i, k, l}
Hallar:  ( △ )△ , ∩ ( − )Cc Ac Bc Cc Ac Bc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {12, 18, 24, 36, 42, 48, 54}
= {6, 12, 18, 24, 36, 42, 48, 54, 60, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
Hallar:  ( ∩ ) ∪ , ∪ ( ∪ )Ac Bc Cc Ac Bc Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 12, 15, 18, 21, 24, 27, 30, 33}
= {3, 12, 24, 27, 36}
= {3, 6, 9, 12, 15, 24, 30, 33}
Hallar:  (C− ) − , C∪ ( △ )Bc Ac Bc Ac
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, o, p, q, r, s, t, u, w, x}
= {m, n, o, p, u, v, w, x}
= {m, n, o, p, r, s, u, v, x}
Hallar:  ( ∪ ) − , − ( ∪ )Bc Cc Ac Bc Cc Ac
201). Dado el conjunto universal:
y los subconjuntos:
202). Dado el conjunto universal:
y los subconjuntos:
203). Dado el conjunto universal:
y los subconjuntos:
204). Dado el conjunto universal:
y los subconjuntos:
205). Dado el conjunto universal:
y los subconjuntos:
206). Dado el conjunto universal:
y los subconjuntos:
207). Dado el conjunto universal:
y los subconjuntos:
208). Dado el conjunto universal:
y los subconjuntos:
209). Dado el conjunto universal:
y los subconjuntos:
210). Dado el conjunto universal:
y los subconjuntos:
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {9, 15, 21, 24, 27, 30, 33, 36}
= {3, 12, 15, 33, 36}
= {9, 12, 15, 18, 24, 27, 30, 33, 36}
Hallar:  (A∪ ) −B, A∪ ( ∪B)Cc Cc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 40, 50, 70, 90}
= {10, 30, 60, 70, 80, 100}
= {10, 20, 60, 70, 100}
Hallar:  (A∩ ) ∪ , A△ ( △ )Cc Bc Cc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 8, 12, 16, 20, 24, 32, 36, 40, 44, 48}
= {4, 8, 16, 20, 24, 28, 32, 40, 44, 48}
= {4, 8, 12, 16, 20, 28, 32, 36, 40, 44, 48}
Hallar:  ( ∪ )△A, − ( ∩A)Cc Bc Cc Bc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 27, 36, 45, 54, 63, 72, 90}
= {36, 45, 54, 72, 81, 90}
= {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
Hallar:  (C△A) −B, C△ (A∩B)
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 9, 12, 15, 18, 21, 30, 33, 36}
= {9, 18, 21, 24, 27, 30, 33}
= {3, 6, 9, 12, 15, 24, 27, 30, 33, 36}
Hallar:  ( ∩B) ∩A, − (B∪A)C
c Cc
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 35, 70, 77, 84}
= {21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {14, 28, 35, 42, 49, 56, 77, 84}
Hallar:  (C∪B)△ , C∩ (B△ )A
c Ac
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 9, 15, 18, 24, 27, 33, 36}
= {24, 27, 30, 33, 36}
= {6, 9, 18, 24, 27, 30, 36}
Hallar:  (A− ) ∩C, A△ ( ∪C)Bc Bc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 55, 66, 77, 88, 99, 110}
= {11, 22, 33, 44, 55, 77, 88, 99, 110}
= {11, 22, 66, 77, 110}
Hallar:  ( ∪C) −A, ∪ (C−A)Bc Bc
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 10, 15, 25, 40, 45, 50, 55, 60}
= {5, 15, 20, 25, 35, 45, 50, 55, 60}
= {5, 10, 15, 20, 30, 35, 40, 50, 55, 60}
Hallar:  ( ∩ ) −A, ∩ ( −A)Bc Cc Bc Cc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
= {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
= {8, 16, 24, 48, 56, 64, 72, 80, 88}
Hallar:  (B−A) ∩C, B∪ (A−C)
211). Dado el conjunto universal:
y los subconjuntos:
212). Dado el conjunto universal:
y los subconjuntos:
213). Dado el conjunto universal:
y los subconjuntos:
214). Dado el conjunto universal:
y los subconjuntos:
215). Dado el conjunto universal:
y los subconjuntos:
216). Dado el conjunto universal:
y los subconjuntos:
217). Dado el conjunto universal:
y los subconjuntos:
218). Dado el conjunto universal:
y los subconjuntos:
219). Dado el conjunto universal:
y los subconjuntos:
220). Dado el conjunto universal:
y los subconjuntos:
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 4, 6, 8, 10, 12, 14, 20, 22, 24}
= {2, 14, 16, 18, 20, 24}
= {6, 8, 16, 18, 22}
Hallar:  (C∪ ) ∩ , C∪ ( △ )Bc Ac Bc Ac
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {a, g, i, j, k}
= {a, b, c, d, e, f , g, h, i, j, k, l}
= {b, c, d, e, f , g, h, i, j, k}
Hallar:  ( △A) −B, − (A∩B)Cc Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 9, 12, 18, 24}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
= {6, 9, 12, 18, 21, 27, 30, 33}
Hallar:  (C△ ) ∩ , C△ ( ∪ )Bc Ac Bc Ac
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {4, 6, 8, 10, 16, 20, 22}
= {2, 4, 10, 20, 22}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Hallar:  (C∩ ) ∪ , C△ ( − )Bc Ac Bc Ac
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 28, 56, 63, 70}
= {7, 14, 28, 56, 70, 77}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
Hallar:  (A∪ ) ∩B, A− ( ∪B)C
c Cc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 20, 30, 40, 50, 60, 70, 90, 100}
= {10, 20, 30, 60, 70, 100}
Hallar:  ( ∩ )△ , ∪ ( − )C
c Ac Bc Cc Ac Bc
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 21, 28, 35, 56, 63, 70, 84}
= {7, 28, 35, 42, 49, 77, 84}
= {7, 14, 21, 28, 35, 49, 56, 63, 70, 77, 84}
Hallar:  ( −C)△B, − (C∪B)Ac Ac
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {4, 6, 8, 10, 12, 14, 16, 18, 22, 24}
= {2, 4, 6, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 6, 8, 10, 14, 18, 20, 22, 24}
Hallar:  (B− )△C, B△ ( −C)Ac Ac
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 14, 28, 35, 42, 49, 56, 70, 77, 84}
= {7, 14, 21, 28, 35, 77, 84}
Hallar:  ( ∩C)△ , ∪ (C− )Ac Bc Ac Bc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 48, 60, 72, 96, 108, 120}
= {12, 24, 48, 60, 72, 84, 96, 108}
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
Hallar:  ( ∩A) − , − (A∪ )BcCc Bc Cc
221). Dado el conjunto universal:
y los subconjuntos:
222). Dado el conjunto universal:
y los subconjuntos:
223). Dado el conjunto universal:
y los subconjuntos:
224). Dado el conjunto universal:
y los subconjuntos:
225). Dado el conjunto universal:
y los subconjuntos:
226). Dado el conjunto universal:
y los subconjuntos:
227). Dado el conjunto universal:
y los subconjuntos:
228). Dado el conjunto universal:
y los subconjuntos:
229). Dado el conjunto universal:
y los subconjuntos:
230). Dado el conjunto universal:
y los subconjuntos:
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {n, o, p, r, s, u, w, x}
= {n, p, q, r, t, u, v, x}
= {m, p, q, r, s, t, u, v, w, x}
Hallar:  ( △C) ∩B, ∩ (C△B)Ac Ac
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {10, 25, 30, 35, 40, 60}
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
= {10, 25, 30, 50, 60}
Hallar:  ( △ ) −B, ∩ ( −B)Ac Cc Ac Cc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
= {18, 45, 54, 63, 81, 90}
= {9, 18, 27, 36, 54, 63, 72, 81, 90}
Hallar:  ( −C) ∪B, △ (C∪B)Ac Ac
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, o, p, q, s, t, u, w, x}
= {m, n, o, p, q, r, s, t, u, v, w}
= {m, n, q, r, s, w}
Hallar:  (B∩C) ∪A, B∩ (C−A)
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 4, 6, 12, 16, 20, 22, 24}
= {2, 4, 6, 8, 10, 16, 18, 20, 24}
= {2, 4, 10, 12, 18, 24}
Hallar:  ( − )△A, ∩ ( △A)C
c Bc Cc Bc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 60, 108, 120}
= {12, 24, 36, 60, 84, 96, 120}
= {12, 24, 36, 60, 72, 84, 96, 108, 120}
Hallar:  ( ∪C)△ , − (C∩ )A
c Bc Ac Bc
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, p, r, v, x}
= {p, r, u, v, w}
= {m, o, q, r, s, t, u, v, x}
Hallar:  ( ∪A) ∪C, − (A∪C)Bc Bc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {6, 9, 12, 15, 21, 27, 30, 33, 36}
= {6, 9, 18, 21, 24, 27}
= {6, 9, 18, 21, 24, 30, 33}
Hallar:  ( −A)△B, ∪ (A△B)Cc Cc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 8, 12, 24, 28, 36, 40, 44, 48}
= {4, 8, 12, 16, 20, 24, 28, 40, 44, 48}
= {12, 20, 24, 28, 32, 44, 48}
Hallar:  ( ∩A) − , △ (A△ )Bc Cc Bc Cc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 6, 8, 10, 12}
= {2, 12, 14, 16, 20}
= {2, 4, 6, 8, 10, 14, 16, 18, 22, 24}
Hallar:  (C− ) − , C− ( △ )Ac Bc Ac Bc
231). Dado el conjunto universal:
y los subconjuntos:
232). Dado el conjunto universal:
y los subconjuntos:
233). Dado el conjunto universal:
y los subconjuntos:
234). Dado el conjunto universal:
y los subconjuntos:
235). Dado el conjunto universal:
y los subconjuntos:
236). Dado el conjunto universal:
y los subconjuntos:
237). Dado el conjunto universal:
y los subconjuntos:
238). Dado el conjunto universal:
y los subconjuntos:
239). Dado el conjunto universal:
y los subconjuntos:
240). Dado el conjunto universal:
y los subconjuntos:
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {c, e, f , g, h, i, j, l}
= {c, d, f , g, h, i, j}
= {d, e, f , i, j, k, l}
Hallar:  (A∩B) ∩ , A△ (B− )Cc Cc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 18, 24, 42, 54, 66, 72}
= {6, 18, 24, 48, 54, 60, 72}
= {6, 12, 18, 24, 30, 36, 48, 66}
Hallar:  ( ∩C) ∪A, △ (C−A)Bc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 16, 20, 24, 32, 40, 48}
= {4, 16, 24, 28, 32, 36, 40, 44}
= {4, 8, 16, 20, 24, 32, 44}
Hallar:  ( ∩C) − , ∪ (C∩ )Ac Bc Ac Bc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 12, 18, 24, 27, 30}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30}
= {3, 6, 9, 12, 15, 21, 24, 27, 30, 36}
Hallar:  (A∩ ) −C, A∩ ( △C)Bc Bc
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {a, b, c, d, e, g, h, k}
= {a, b, f , h, j, k, l}
= {a, b, c, d, e, h, i, j, k}
Hallar:  (B△ ) − , B− ( ∪ )A
c Cc Ac Cc
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, o, p, q, r, s, t, u, v, w, x}
= {m, n, o, p, q, r, s, t, v, w, x}
= {o, p, q, r, w}
Hallar:  (B△A) ∩C, B∪ (A∩C)
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 33, 44, 55, 66, 77, 99}
= {11, 44, 55, 66, 77, 88, 99}
= {11, 22, 33, 55, 77, 99}
Hallar:  (B∩ )△C, B− ( ∩C)Ac Ac
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {3, 5, 11, 13, 37}
= {5, 11, 13, 17, 19, 23, 29, 37}
= {2, 7, 13, 23, 29, 31, 37}
Hallar:  (B∩ ) −C, B− ( −C)Ac Ac
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 28, 35, 77, 84}
= {7, 21, 28, 35, 42, 56, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
Hallar:  (B−C) ∩ , B∪ (C∪ )Ac Ac
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 60, 72, 120}
= {36, 48, 60, 84, 96, 108, 120}
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
Hallar:  ( − )△ , ∪ ( ∩ )Cc Ac Bc Cc Ac Bc
241). Dado el conjunto universal:
y los subconjuntos:
242). Dado el conjunto universal:
y los subconjuntos:
243). Dado el conjunto universal:
y los subconjuntos:
244). Dado el conjunto universal:
y los subconjuntos:
245). Dado el conjunto universal:
y los subconjuntos:
246). Dado el conjunto universal:
y los subconjuntos:
247). Dado el conjunto universal:
y los subconjuntos:
248). Dado el conjunto universal:
y los subconjuntos:
249). Dado el conjunto universal:
y los subconjuntos:
250). Dado el conjunto universal:
y los subconjuntos:
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 35, 49, 56, 70, 77, 84}
= {7, 35, 42, 56, 63, 77}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
Hallar:  ( −A) ∩C, ∩ (A△C)Bc Bc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {18, 36, 54, 63, 72, 90}
= {18, 27, 36, 54, 72, 81, 90}
= {9, 18, 36, 45, 54, 63, 72, 81}
Hallar:  ( ∪C) −B, ∪ (C∪B)Ac Ac
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {27, 36, 45, 63, 72, 81}
= {9, 18, 36, 45, 54, 81}
= {9, 18, 27, 36, 45, 54, 63, 81, 90}
Hallar:  ( − ) ∪C, △ ( ∩C)Ac Bc Ac Bc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 36, 60, 72, 96}
= {12, 36, 48, 60, 72, 84, 96, 108, 120}
Hallar:  (C− ) − , C△ ( △ )Ac Bc Ac Bc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {18, 36, 45, 63, 72, 81, 90}
= {9, 27, 36, 45, 54, 63, 72, 81, 90}
= {9, 18, 27, 36, 45, 54}
Hallar:  ( △ ) − , △ ( ∪ )A
c Bc Cc Ac Bc Cc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {4, 8, 10, 12, 16, 18, 20, 22}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
= {4, 6, 8, 10, 12, 16, 18, 20, 22, 24}
Hallar:  ( △ ) −C, ∪ ( ∩C)A
c Bc Ac Bc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {20, 30, 40, 60, 70, 80, 90, 100}
= {20, 30, 40, 50, 60, 80, 100}
= {10, 20, 30, 50, 60}
Hallar:  (C∩ ) − , C− ( △ )Ac Bc Ac Bc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 11, 17, 19, 29, 31, 37}
= {2, 5, 7, 13, 17}
= {3, 7, 11, 13, 17, 19, 29}
Hallar:  ( ∪ ) ∩ , ∪ ( ∪ )Bc Ac Cc Bc Ac Cc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 36, 48, 60, 84, 96, 108, 120}
= {12, 24, 48, 60, 72, 84, 96, 108, 120}
Hallar:  (A△C) − , A− (C∪ )Bc Bc
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 10, 20, 25, 30, 35, 40, 45, 50, 55, 60}
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
= {10, 15, 30, 40, 55}
Hallar:  (A∩C)△B, A∩ (C∪B)
251). Dado el conjunto universal:
y los subconjuntos:
252). Dado el conjunto universal:
y los subconjuntos:
253). Dado el conjunto universal:
y los subconjuntos:
254). Dado el conjunto universal:
y los subconjuntos:
255). Dado el conjunto universal:
y los subconjuntos:
256). Dado el conjunto universal:
y los subconjuntos:
257). Dado el conjunto universal:
y los subconjuntos:
258). Dado el conjunto universal:
y los subconjuntos:
259). Dado el conjunto universal:
y los subconjuntos:
260). Dado el conjunto universal:
y los subconjuntos:
U= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 48, 60, 72, 84, 96, 120}
= {24, 36, 48, 84, 96, 108, 120}
= {12, 24, 48, 60, 72, 84, 96, 108, 120}
Hallar:  ( −C) ∩ , − (C∪ )Bc Ac Bc Ac
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 11, 17, 19, 29, 31}
= {2, 3, 5, 11, 13, 17, 29, 31}
= {2, 3, 7, 11, 13, 17, 19, 23, 29, 31, 37}
Hallar:  ( ∩ )△B, ∪ ( △B)Cc Ac Cc Ac
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 60, 70, 80, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 20, 70, 80, 90}
Hallar:  (A∩ ) −C, A∪ ( △C)Bc Bc
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {a, b, c, d, e, f , g, h, i, j, k, l}
= {b, c, d, e, f , g, i, j, k}
= {b, e, h, i, l}
Hallar:  (A△C)△B, A∪ (C∩B)
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {b, c, d, e, g, h, i, j, k}
= {a, c, d, e, f , g, h, j, k}
= {c, d, h, j, k}
Hallar:  ( −B) ∩ , − (B∩ )A
c Cc Ac Cc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {24, 30, 36, 42, 48, 54, 60, 72}
= {6, 24, 54, 60, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
Hallar:  ( ∪ ) − , − ( ∩ )C
c Ac Bc Cc Ac Bc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 44, 55, 66, 88, 110}
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
= {11, 33, 44, 55, 110}
Hallar:  ( ∩A) ∪ , ∪ (A△ )Cc Bc Cc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
= {8, 24, 28, 40, 44}
= {8, 12, 16, 20, 28, 40}
Hallar:  (B− ) −C, B△ ( ∩C)Ac Ac
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {n, o, q, r, s, u, w, x}
= {m, n, o, p, q, r, s, t, u, v, w, x}
= {m, n, p, q, r, s, t, u, v, w, x}
Hallar:  ( −B)△ , − (B− )Ac Cc Ac Cc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 18, 27, 54, 72, 81, 90}
= {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
= {9, 18, 27, 45, 54, 63, 90}
Hallar:  (B−A) − , B∪ (A∪ )Cc Cc
261). Dado el conjunto universal:
y los subconjuntos:
262). Dado el conjunto universal:
y los subconjuntos:
263). Dado el conjunto universal:
y los subconjuntos:
264). Dado el conjunto universal:
y los subconjuntos:
265). Dado el conjunto universal:
y los subconjuntos:
266). Dado el conjunto universal:
y los subconjuntos:
267). Dado el conjunto universal:
y los subconjuntos:
268). Dado el conjunto universal:
y los subconjuntos:
269). Dado el conjunto universal:
y los subconjuntos:
270). Dado el conjunto universal:
y los subconjuntos:
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 16, 20, 24, 28, 32, 36, 40, 44}
= {8, 12, 16, 20, 24, 28, 32, 40, 44, 48}
= {12, 16, 24, 28, 32, 36, 40, 44, 48}
Hallar:  ( ∩A) ∩C, ∩ (A∪C)Bc Bc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 24, 36, 48, 60, 72, 84, 96, 120}
= {12, 36, 48, 60, 84, 96}
Hallar:  ( ∩C) ∩A, ∪ (C∩A)Bc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 12, 24, 28, 36, 40, 44, 48}
= {4, 12, 16, 20, 28, 32, 36, 44, 48}
= {4, 8, 12, 20, 24, 28, 32, 36, 40, 44, 48}
Hallar:  (C∩A) − , C− (A∪ )Bc Bc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 40, 50, 60, 90}
= {10, 30, 40, 60, 70, 80, 90, 100}
Hallar:  (C− ) ∩B, C△ ( △B)Ac Ac
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 55, 66, 77, 88, 110}
= {11, 33, 44, 77, 88}
= {11, 33, 44, 77, 99, 110}
Hallar:  ( ∪A) ∪C, − (A△C)Bc Bc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 7, 11, 13, 37}
= {17, 19, 23, 29, 37}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
Hallar:  ( ∩ ) −A, − ( −A)C
c Bc Cc Bc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 72}
= {6, 18, 30, 36, 54, 60, 72}
= {6, 18, 24, 30, 36, 42, 48, 54, 66, 72}
Hallar:  (C∩ ) −A, C△ ( △A)Bc Bc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {20, 30, 40, 70, 80, 90}
= {40, 60, 70, 80, 90, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
Hallar:  (A∩B) ∪ , A∪ (B∪ )Cc Cc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 13, 17, 19, 29, 31, 37}
= {2, 3, 7, 11, 13, 19, 23, 29, 31, 37}
= {2, 3, 7, 11, 13, 17, 19, 23, 29, 31, 37}
Hallar:  (A∩C) ∩ , A△ (C∩ )Bc Bc
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {a, b, c, d, e, f , g, h, i, j, k, l}
= {a, b, c, d, e, f , g, h, i, j, k, l}
= {a, b, c, d, f , g, h, i, j, l}
Hallar:  ( △B)△C, △ (B∪C)Ac Ac
271). Dado el conjunto universal:
y los subconjuntos:
272). Dado el conjunto universal:
y los subconjuntos:
273). Dado el conjunto universal:
y los subconjuntos:
274). Dado el conjunto universal:
y los subconjuntos:
275). Dado el conjunto universal:
y los subconjuntos:
276). Dado el conjunto universal:
y los subconjuntos:
277). Dado el conjunto universal:
y los subconjuntos:
278). Dado el conjunto universal:
y los subconjuntos:
279). Dado el conjunto universal:
y los subconjuntos:
280). Dado el conjunto universal:
y los subconjuntos:
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 6, 10, 14, 22}
= {2, 8, 10, 12, 14, 16, 18, 20, 22, 24}
= {4, 8, 14, 20, 22}
Hallar:  (C∩A) ∩ , C△ (A△ )Bc Bc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {4, 6, 8, 14, 16, 18, 22, 24}
= {2, 6, 10, 16, 22}
= {2, 6, 8, 10, 12, 18, 20, 24}
Hallar:  ( ∪C) ∩ , ∪ (C∪ )Bc Ac Bc Ac
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 33, 44, 66, 110}
= {22, 55, 77, 88, 110}
= {11, 22, 33, 66, 77, 88, 110}
Hallar:  (C∩ ) ∪ , C△ ( ∪ )Ac Bc Ac Bc
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {21, 28, 42, 49, 56, 63, 84}
= {7, 21, 28, 35, 63}
= {7, 14, 21, 28, 35, 42, 49, 56, 70, 77, 84}
Hallar:  ( − )△ , ∪ ( ∩ )Cc Ac Bc Cc Ac Bc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 3, 5, 7, 13, 17, 19, 23, 29, 31, 37}
= {2, 3, 5, 7, 17, 19, 23, 29, 37}
Hallar:  (A△ )△C, A△ ( ∩C)Bc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 12, 20, 28, 36, 40, 48}
= {4, 12, 16, 24, 28, 36, 40, 44}
= {4, 8, 12, 20, 24, 28, 32, 36, 40, 44}
Hallar:  (B△C) − , B∩ (C− )A
c Ac
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 8, 12, 16, 18}
= {2, 4, 6, 8, 12, 14, 16, 18, 20}
= {2, 4, 6, 12, 14, 20}
Hallar:  ( ∩ ) −C, ∪ ( −C)Bc Ac Bc Ac
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 44, 55, 77, 110}
= {11, 44, 66, 77, 88}
= {11, 22, 33, 55, 66, 77, 99}
Hallar:  ( ∩ ) −A, △ ( ∪A)Bc Cc Bc Cc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 60, 72, 84, 96, 108}
= {24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 36, 48, 60, 72, 84, 96, 108, 120}
Hallar:  (B∪ )△ , B△ ( △ )Ac Cc Ac Cc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 36, 48, 60, 72, 84, 96, 120}
= {12, 36, 60, 72, 84, 108, 120}
Hallar:  (C△ ) − , C∩ ( ∪ )Ac Bc Ac Bc
281). Dado el conjunto universal:
y los subconjuntos:
282). Dado el conjunto universal:
y los subconjuntos:
283). Dado el conjunto universal:
y los subconjuntos:
284). Dado el conjunto universal:
y los subconjuntos:
285). Dado el conjunto universal:
y los subconjuntos:
286). Dado el conjunto universal:
y los subconjuntos:
287). Dado el conjunto universal:
y los subconjuntos:
288). Dado el conjunto universal:
y los subconjuntos:
289). Dado el conjunto universal:
y los subconjuntos:
290). Dado el conjunto universal:
y los subconjuntos:
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 49, 56, 63, 70, 77, 84}
= {7, 28, 49, 56, 77}
= {28, 42, 49, 56, 63, 70, 77}
Hallar:  (A∩C) ∩ , A△ (C△ )Bc Bc
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, o, p, q, r, s, t, u}
= {m, o, p, q, r, s, u, v, w, x}
= {n, p, q, r, s, u, x}
Hallar:  (C∪ ) − , C∩ ( △ )Bc Ac Bc Ac
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14,35, 49, 70, 84}
= {14, 21, 35, 49, 56, 70, 77, 84}
= {7, 14, 21, 28, 63, 70, 77, 84}
Hallar:  ( − )△A, △ ( ∩A)Cc Bc Cc Bc
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 28, 35, 63, 77, 84}
= {7, 14, 21, 28, 49, 56, 63, 70, 77, 84}
= {14, 21, 28, 35, 42, 49, 70, 77, 84}
Hallar:  (B△A)△C, B△ (A∩C)
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 48, 60, 84, 96, 108, 120}
= {12, 24, 36, 48, 60, 72, 84, 96, 108}
= {12, 24, 36, 60, 84, 108}
Hallar:  ( ∪ )△ , ∪ ( ∩ )Bc A
c Cc Bc Ac Cc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 30, 50, 60, 100}
= {10, 20, 30, 40, 70, 100}
= {10, 20, 30, 40, 50, 70, 80, 90, 100}
Hallar:  (C∪B) − , C△ (B∪ )A
c Ac
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {6, 9, 12, 15, 18, 24, 30, 33, 36}
= {12, 21, 24, 30, 33}
= {6, 15, 24, 27, 30, 33}
Hallar:  ( −C) −A, ∪ (C∩A)Bc Bc
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 10, 25, 35, 50, 55, 60}
= {10, 15, 30, 35, 40, 45, 55, 60}
= {5, 15, 20, 30, 35, 40, 50, 55, 60}
Hallar:  (B△ )△A, B− ( ∩A)Cc Cc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
= {11, 22, 33, 44, 55, 66, 88, 99, 110}
Hallar:  (C∪ ) ∩A, C∩ ( −A)Bc Bc
U = {a, b, c, d, e, f , g, h, i, j, k, l}
A
B
C
= {a, b, c, g, i, l}
= {a, b, d, e, f , g, h, i, j, l}
= {a, b, c, d, e, f , g, h, i, k, l}
Hallar:  ( ∪C)△ , ∪ (C△ )Ac Bc Ac Bc
291). Dado el conjunto universal:
y los subconjuntos:
292). Dado el conjunto universal:
y los subconjuntos:
293). Dado el conjunto universal:
y los subconjuntos:
294). Dado el conjunto universal:
y los subconjuntos:
295). Dado el conjunto universal:
y los subconjuntos:
296). Dado el conjunto universal:
y los subconjuntos:
297). Dado el conjunto universal:
y los subconjuntos:
298). Dado el conjunto universal:
y los subconjuntos:
299). Dado el conjunto universal:
y los subconjuntos:
300). Dado el conjunto universal:
y los subconjuntos:
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
= {3, 6, 12, 15, 18, 21, 24, 30, 33, 36}
= {3, 9, 12, 18, 21, 24, 27, 30, 33, 36}
Hallar:  (B∪C) ∩ , B− (C△ )Ac Ac
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, o, p, q, r, t, v, x}
= {m, n, o, p, q, r, s, t, u, v, w, x}
= {m, n, t, v, w}
Hallar:  ( −B)△ , △ (B∪ )Ac Cc Ac Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 12, 15, 18, 24, 30, 33, 36}
= {3, 6, 24, 33, 36}
= {3, 6, 12, 15, 18, 24}
Hallar:  (C∩B) −A, C− (B∩A)
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
= {5, 15, 20, 30, 60}
= {5, 10, 25, 40, 45, 60}
Hallar:  (A△C) − , A△ (C∩ )Bc Bc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 48, 72, 84, 108}
= {36, 48, 60, 96, 108}
= {12, 24, 48, 72, 84, 96, 120}
Hallar:  ( ∩ )△A, ∪ ( ∩A)Bc C
c Bc Cc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {3, 5, 7, 11, 13, 19, 29, 31, 37}
= {2, 3, 5, 7, 11, 13, 17, 29, 31, 37}
= {2, 3, 7, 13, 19, 23, 29, 37}
Hallar:  (A∩C) ∩ , A∪ (C∪ )Bc Bc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 50, 60, 70, 90, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 100}
= {10, 20, 30, 50, 60, 70, 90}
Hallar:  ( − )△A, ∪ ( △A)Cc Bc Cc Bc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 33, 55, 66, 77, 99}
= {33, 44, 55, 66, 77, 88, 99, 110}
= {11, 22, 33, 44, 55, 77, 99, 110}
Hallar:  ( ∩ )△ , △ ( △ )Ac Cc Bc Ac Cc Bc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {18, 27, 54, 63, 81, 90}
= {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
= {9, 18, 27, 36, 54, 63, 72, 81, 90}
Hallar:  (A−C) ∪ , A− (C△ )Bc Bc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {20, 30, 40, 50, 60, 70}
= {10, 20, 30, 40, 50, 60, 90, 100}
= {10, 20, 40, 50, 60, 70, 80, 90}
Hallar:  ( − ) ∩C, − ( △C)Ac Bc Ac Bc
301). Dado el conjunto universal:
y los subconjuntos:
302). Dado el conjunto universal:
y los subconjuntos:
303). Dado el conjunto universal:
y los subconjuntos:
304). Dado el conjunto universal:
y los subconjuntos:
305). Dado el conjunto universal:
y los subconjuntos:
306). Dado el conjunto universal:
y los subconjuntos:
307). Dado el conjunto universal:
y los subconjuntos:
308). Dado el conjunto universal:
y los subconjuntos:
309). Dado el conjunto universal:
y los subconjuntos:
310). Dado el conjunto universal:
y los subconjuntos:
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 8, 10, 16, 18, 20}
= {2, 4, 6, 8, 10, 12, 14, 18, 22}
Hallar:  (B∪ ) − , B△ ( ∪ )Ac Cc Ac Cc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 7, 13, 23, 29}
= {2, 3, 5, 7, 11, 13, 19, 23, 29, 37}
= {7, 11, 17, 19, 23, 31}
Hallar:  ( △A) −C, − (A∩C)Bc Bc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 7, 11, 17, 19, 29, 37}
= {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 3, 5, 11, 13, 17, 19, 23, 29, 31}
Hallar:  (A△B) ∪ , A△ (B− )Cc Cc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 44, 55, 66, 110}
= {33, 44, 66, 77, 88, 99, 110}
= {11, 22, 33, 44, 55, 66, 77, 88, 99}
Hallar:  ( ∪A) −C, ∪ (A−C)Bc Bc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 36, 60, 84, 120}
= {36, 48, 60, 96, 108, 120}
Hallar:  (C△ )△A, C∩ ( △A)Bc Bc
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 42, 49, 56, 63, 77}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 28, 35, 42, 56}
Hallar:  (C△ ) ∩ , C∪ ( ∩ )A
c Bc Ac Bc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 9, 12, 15, 18, 24, 27, 36}
= {3, 6, 12, 18, 21, 24, 27, 33, 36}
= {3, 15, 18, 21, 24, 27, 30, 33, 36}
Hallar:  (A△ ) ∩ , A∪ ( ∩ )Cc Bc Cc Bc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {6, 9, 12, 15, 21, 33}
= {3, 6, 9, 15, 18, 21, 24, 27, 30, 33}
= {3, 9, 24, 27, 33}
Hallar:  ( ∩ ) −C, − ( △C)Bc Ac Bc Ac
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 18, 27, 45, 54, 90}
= {9, 18, 36, 45, 54, 63, 72, 90}
= {9, 18, 27, 36, 54, 63, 72, 81, 90}
Hallar:  (A△C) ∩ , A− (C△ )Bc Bc
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, o, p, q, r, s, u, w, x}
= {m, n, o, p, q, r, s, t, u, v, w, x}
= {n, p, q, r, s, w}
Hallar:  (B∩C) ∪ , B∩ (C− )Ac Ac
311). Dado el conjunto universal:
y los subconjuntos:
312). Dado el conjunto universal:
y los subconjuntos:
313). Dado el conjunto universal:
y los subconjuntos:
314). Dado el conjunto universal:
y los subconjuntos:
315). Dado el conjunto universal:
y los subconjuntos:
316). Dado el conjunto universal:
y los subconjuntos:
317). Dado el conjunto universal:
y los subconjuntos:
318). Dado el conjunto universal:
y los subconjuntos:
319). Dado el conjunto universal:
y los subconjuntos:
320). Dado el conjunto universal:
y los subconjuntos:
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, o, p, q, r, s, t, u, v, x}
= {m, n, o, p, q, r, s, t, u, v, w, x}
= {m, n, o, p, q, r, s, t, u, v, w, x}
Hallar:  ( − ) −B, △ ( ∪B)Ac Cc Ac Cc
U = {m, n, o, p, q, r, s, t, u, v, w, x}
A
B
C
= {m, n, o, q, r, s, t, u, v, w, x}
= {m, o, p, s, v, x}
= {m, p, t, u, v}
Hallar:  ( △ ) ∪ , ∪ ( − )Cc Bc Ac Cc Bc Ac
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 55, 77, 88, 99}
= {11, 22, 33, 66, 77, 88, 99, 110}
= {11, 22, 33, 44, 66, 77, 88, 110}
Hallar:  (B△ ) − , B△ ( ∪ )Cc Ac Cc Ac
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 30, 40, 60, 70, 80, 90, 100}
= {10, 20, 40, 70, 90}
Hallar:  (B∩A) ∩C, B△ (A△C)
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 7, 13, 17, 19, 23, 31, 37}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31}
= {3, 5, 7, 11, 17, 23,