200 ejercicios sobre Operaciones entre Conjuntos resueltos paso a paso con procedimientos.

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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, 37}
= {2, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
Hallar:  ( ∩ )∩A, △ ( −A)Cc Bc Cc Bc
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {a, d, e, g,h, i}
= {a, b, c, e,h, i,k, l}
= {c, d, e, f , g,h, i, j,k}
Hallar:  (A∪C)△ , A−(C∪ )Bc Bc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 70, 80, 100}
= {10, 20, 30, 40, 70, 80, 90, 100}
= {10, 30, 70, 80, 90, 100}
Hallar:  (B∪C)− , B∪ (C△ )Ac Ac
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 18, 24, 30, 42, 48, 54, 60, 66, 72}
= {6, 12, 30, 36, 54}
= {6, 12, 24, 42, 48, 54, 60, 66, 72}
Hallar:  ( ∪A)∪B, ∩ (A△B)Cc Cc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 16, 20, 24, 28, 32, 40, 44}
= {4, 8, 16, 20, 24, 28, 32, 40, 44, 48}
= {4, 8, 12, 16, 20, 24, 28, 32}
Hallar:  (C∩B)∩A, C△ (B∪A)
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {18, 27, 36, 45, 54, 63}
= {9, 27, 36, 45, 72, 81, 90}
= {9, 18, 54, 63, 72}
Hallar:  (C△B)△ , C△ (B− )Ac Ac
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 27, 36, 45, 54, 63, 72}
= {9, 18, 27, 36, 45, 63, 81, 90}
= {18, 27, 45, 63, 72, 90}
Hallar:  ( ∩A)△ , ∪ (A∩ )Bc Cc Bc Cc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {32, 40, 56, 64, 72}
= {8, 16, 32, 40, 48, 56, 64, 72, 80, 96}
= {8, 24, 40, 72, 80, 88, 96}
Hallar:  ( △ )∪ , △ ( ∪ )Cc Bc Ac Cc Bc Ac
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {20, 30, 40, 50, 60, 70, 80, 100}
= {10, 30, 60, 70, 90, 100}
= {10, 20, 30, 40, 50, 60, 80, 90, 100}
Hallar:  ( ∩ )−A, △ ( △A)Cc Bc Cc Bc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 18, 24, 36, 48, 54, 60, 66, 72}
= {6, 12, 30, 60, 72}
= {6, 12, 18, 24, 30, 42, 48, 54, 60, 66, 72}
Hallar:  ( ∩A)− , ∪ (A− )Bc Cc Bc Cc
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 = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {12, 36, 42, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
= {6, 24, 30, 36, 48}
Hallar:  ( ∩ )△ , −( ∪ )Cc Bc Ac Cc Bc 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, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 77, 84}
Hallar:  (B△C)∩A, B∪ (C∪A)
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}
= {e, f ,h, i,k, l}
= {a, b, c, d, e, g, i, j}
Hallar:  ( − )− , △ ( △ )Cc Ac Bc Cc Ac Bc
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, 15, 18, 21, 24, 27, 30, 33, 36}
= {3, 6, 9, 12, 15, 27, 30, 33}
Hallar:  (C−B)∪A, C△ (B−A)
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 35, 49, 70, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {14, 21, 49, 56, 77, 84}
Hallar:  ( △C)∪B, ∪ (C△B)Ac Ac
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {14, 28, 42, 63, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 21, 35, 63, 70, 77, 84}
Hallar:  ( ∪B)−A, ∪ (B∩A)Cc Cc
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 21, 28, 35, 42, 49, 56, 70, 77, 84}
= {14, 21, 28, 35, 42, 56, 63, 70, 77, 84}
= {7, 14, 21, 28, 49, 56, 63, 70, 77}
Hallar:  ( ∩ )− , −( △ )Ac Bc Cc Ac Bc Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {6, 12, 21, 24, 27}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
= {6, 12, 24, 27, 30, 33, 36}
Hallar:  (B△ )△C, B∪ ( ∩C)Ac Ac
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {18, 30, 48, 60, 66, 72}
= {6, 24, 42, 54, 66}
= {6, 12, 18, 30, 36, 42, 48, 54, 60, 72}
Hallar:  (A∪B)−C, A∩ (B∩C)
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, 18, 24, 30, 36, 42, 48, 54, 66, 72}
= {6, 24, 30, 36, 42, 48, 54, 66, 72}
Hallar:  (A△ )−B, A∪ ( ∩B)Cc 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 = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 24, 30, 48, 60}
= {12, 24, 30, 36, 42, 48, 54, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 54, 72}
Hallar:  (C∪A)∩ , C∪ (A− )Bc Bc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 24, 36, 48, 54}
= {6, 18, 60, 66, 72}
= {6, 12, 24, 30, 36, 42, 48, 54, 60, 66, 72}
Hallar:  (C∩ )∩A, C−( −A)Bc Bc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 33, 44, 55, 77, 88, 99, 110}
= {11, 44, 55, 66, 77, 88, 99, 110}
= {33, 66, 88, 99, 110}
Hallar:  (A△C)∩ , A△ (C− )Bc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {8, 12, 24, 28, 32, 36, 44}
= {4, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
= {4, 8, 12, 16, 20, 24, 28, 32, 40, 44, 48}
Hallar:  ( −B)− , ∩ (B− )Cc Ac Cc Ac
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 10, 12, 16, 18, 20, 22, 24}
= {2, 4, 6, 8, 10, 12, 14, 16, 20, 22, 24}
= {4, 6, 8, 10, 12, 16, 18, 20, 22, 24}
Hallar:  (A− )∩C, A−( ∩C)Bc Bc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 32, 40, 56, 72, 80}
= {16, 24, 32, 40, 48, 72, 80, 96}
= {8, 16, 24, 32, 64, 72, 80, 88, 96}
Hallar:  (A∪ )△C, A−( ∩C)Bc Bc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 4, 6, 8, 10, 14, 18, 22, 24}
= {2, 6, 8, 12, 14, 16, 18, 20, 22}
= {2, 4, 8, 10, 12, 18}
Hallar:  ( −A)△B, ∪ (A△B)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, 55, 66, 77, 88}
= {22, 33, 44, 55, 66, 77, 88, 99, 110}
Hallar:  (B∪C)∪A, B∪ (C−A)
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 32, 56, 72, 80, 88, 96}
= {8, 16, 40, 48, 80, 88, 96}
= {8, 16, 24, 32, 40, 48, 56, 64, 80, 88, 96}
Hallar:  (C△ )∩B, C−( ∪B)Ac Ac
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 3, 5, 7, 11, 13, 19, 23, 29, 37}
Hallar:  (B−C)△A, B∩ (C−A)
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 = {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, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
Hallar:  ( ∩A)−B, ∩ (A∪B)Cc Cc
U = {m,n, o, p, q, r, s, t,u, v,w,x}
A
B
C
= {m,n, o, p, r, s, t,u, v,w}
= {m,n, o, p, q, r, t,u,x}
= {o, p, q, s,u, v,x}
Hallar:  ( ∪ )∪ , ∪ ( △ )Cc Bc Ac Cc Bc Ac
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 10, 20, 25, 55, 60}
= {5, 10, 15, 20, 40, 45, 50, 55, 60}
= {15, 25, 40, 45, 50}
Hallar:  ( △A)∪ , ∪ (A∩ )Cc Bc Cc Bc
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 42, 49, 56, 70, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 84}
= {14, 21, 28, 56, 70, 84}
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, o, p, q, r, s, t,u, v,w,x}
= {m,n, o, p, q, r, s, t, v,w,x}
= {n, r, s, t,u, v,w}
Hallar:  ( −B)∪A, −(B△A)Cc Cc
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, 12, 16, 20, 32, 40, 44, 48}
= {16, 24, 28, 32, 48}
Hallar:  ( ∪ )∩C, △ ( −C)Ac Bc Ac Bc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 30, 40, 50, 60, 90}
= {10, 30, 40, 50, 70, 80, 100}
= {10, 40, 60, 70, 90}
Hallar:  (C− )∪B, C∪ ( −B)A
c Ac
U = {m,n, o, p, q, r, s, t,u, v,w,x}
A
B
C
= {m,n, o, p, q, r, s,u, v,w,x}
= {m, o, p, q, r, s, t,u, v,x}
= {n, o, p, q, t, v,x}
Hallar:  ( − )∪ , △ ( ∪ )Ac Cc Bc Ac Cc Bc
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {a, b, c, d, e, j,k, l}
= {a, d, e, g,h, l}
= {a, b, c, d, f , g, i, j, l}
Hallar:  ( ∩ )∪ , ∪ ( − )Cc A
c Bc Cc Ac Bc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {8, 12, 14, 16, 22}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 8, 12, 14, 16, 18, 20, 24}
Hallar:  (A△ )∪ , A∩ ( − )Cc Bc Cc Bc
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 = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 50, 60, 70, 80, 90, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 100}
= {10, 20, 30, 70, 90}
Hallar:  (B∪A)− , B−(A∩ )Cc Cc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {6, 9, 12, 15, 21, 27, 33, 36}
= {6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
= {6, 9, 12, 15, 18, 21, 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, 30, 40, 50, 70, 80, 90, 100}
= {10, 20, 30, 60, 80}
= {10, 20, 30, 40, 60, 70, 80, 90, 100}
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, 84, 108}
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
= {24, 36, 48, 60, 72, 84, 108}
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, 66, 77, 88, 110}
= {33, 55, 66, 77, 88, 110}
= {44, 55, 66, 77, 88, 110}
Hallar:  (C△A)∩ , C∩ (A− )Bc Bc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {18, 27, 36, 45, 63, 72, 81, 90}
= {18, 27, 45, 72, 81}
= {9, 18, 36, 45, 72, 90}
Hallar:  ( − )△ , ∪ ( − )Cc Ac Bc Cc Ac Bc
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, b, c, d, e,h, i,k}
= {a, b, e, f , g, i, j,k, l}
Hallar:  ( − )△ , ∩ ( △ )Bc Ac Cc Bc Ac Cc
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 28, 42, 56, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 70, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 84}
Hallar:  ( − )△C, −( −C)Bc Ac Bc Ac
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 48, 60, 84, 96, 108, 120}
= {12, 24, 48, 60, 72, 84, 96, 108, 120}
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
Hallar:  ( ∪ )∩B, △ ( −B)Ac Cc Ac Cc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 44, 55, 66, 77, 88, 99}
= {11, 22, 33, 44, 55, 66, 99, 110}
= {11, 22, 33, 44, 88}
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 = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 60, 70, 80}
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {30, 40, 50, 60, 80, 100}
Hallar:  ( ∩A)−B, △ (A∩B)Cc Cc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 33, 44, 66, 88}
= {22, 33, 44, 55, 66, 99}
= {11, 22, 33, 44, 55, 66, 110}
Hallar:  (A− )∩C, A△ ( ∩C)Bc Bc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 9, 15, 18, 21, 24, 27, 30, 33, 36}
= {15, 18, 24, 27, 30, 36}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
Hallar:  ( − )∩ , −( − )Bc Cc Ac Bc 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, 64, 72, 80, 88, 96}
= {8, 16, 32, 40, 64, 72, 88, 96}
= {16, 24, 40, 56, 64, 72, 80, 88, 96}
Hallar:  ( ∪A)−B, ∩ (A∪B)Cc Cc
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {a, g,h, i, l}
= {a, c, d, e, f ,h, i, j,k, l}
= {a, b, c, d, e, f , g,h, i, j,k, l}
Hallar:  (C△B)−A, C△ (B△A)
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {b, e, f , i, j,k}
= {a, d, e, f , g,h, i, j,k, l}
= {a, b, f , g, i, j,k, l}
Hallar:  (B− )− , B∪ ( − )Ac Cc Ac Cc
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}
= {5, 10, 15, 25, 40, 45, 60}
= {5, 10, 15, 20, 25, 35, 40, 45, 50, 60}
Hallar:  (B∩A)−C, B∩ (A△C)
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {14, 28, 35, 42, 56, 63, 70, 77, 84}
= {7, 14, 21, 28, 49, 63, 70, 84}
= {7, 14, 21, 28, 35, 56, 63, 77, 84}
Hallar:  (C−A)− , C∪ (A△ )Bc Bc
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}
= {3, 6, 15, 18, 21, 24, 27, 30}
Hallar:  ( − )∪C, △ ( −C)Bc Ac Bc Ac
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {b, f , g, i, j, l}
= {a, d, e,h, i, j,k, l}
= {b, d, e, f , g,h, j,k}
Hallar:  (B∪ )−A, B−( ∪A)Cc Cc
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 = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 18, 24, 30, 36, 54, 60, 66, 72}
= {6, 12, 18, 30, 36, 42, 60, 66, 72}
= {6, 24, 36, 42, 54, 72}
Hallar:  ( ∪ )△ , △ ( ∪ )Cc Bc Ac Cc Bc Ac
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, 10, 25, 30, 40, 45}
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
Hallar:  (C∩ )−A, C∪ ( △A)Bc 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, 66}
= {6, 12, 18, 24, 36, 48, 54, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
Hallar:  (B∪ )△C, B△ ( ∩C)Ac Ac
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 23, 37}
= {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 7, 17, 19, 23}
Hallar:  (C△A)△B, C∪ (A∪B)
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 24, 30, 48, 54, 60, 66}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
Hallar:  (B−A)∩ , B−(A− )Cc Cc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {20, 40, 50, 60, 70, 80, 90, 100}
= {20, 30, 40, 50, 60, 70, 80, 90, 100}
= {40, 60, 70, 90, 100}
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, 6, 10, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 6, 8, 10, 12, 14, 16, 20, 22, 24}
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,h, i}
= {a, c, d, f , g,h, i,k}
= {a, b, d, e, f , g,h, i, j, l}
Hallar:  ( ∪ )− , ∪ ( △ )Cc Bc Ac Cc Bc Ac
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 9, 15, 21, 24, 27, 33, 36}
= {3, 6, 9, 18, 24, 33, 36}
= {3, 6, 9, 12, 15, 18, 21, 27, 30, 33, 36}
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, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 21, 35, 42, 49, 63, 70, 77, 84}
= {14, 21, 28, 35, 56, 63, 70, 77, 84}
Hallar:  ( ∪B)− , ∩ (B− )Cc A
c Cc 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 = {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, 24}
= {6, 10, 14, 20, 22, 24}
= {2, 4, 12, 16, 18, 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, 6, 8, 12, 14, 16, 20}
= {2, 8, 14, 22, 24}
= {2, 6, 10, 14, 16, 18, 20, 22}
Hallar:  ( ∪ )∩A, △ ( △A)Cc Bc Cc Bc
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {a, b, c, d, f , i}
= {b, c,h, i, j,k, l}
= {a, c, d, e, i}
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, 6, 8, 10, 12, 14, 18, 20, 22, 24}
= {2, 4, 8, 18, 20, 22, 24}
= {8, 12, 14, 16, 20, 22}
Hallar:  ( △ )− , ∪ ( ∪ )Bc Ac Cc Bc Ac Cc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 40, 90, 100}
= {10, 20, 30, 40, 80, 90, 100}
= {10, 20, 30, 40, 50, 60, 100}
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, e, j, l}
= {a, e, f , g, j,k}
= {c, e, f ,h,k}
Hallar:  (B∪ )−C, B∩ ( △C)Ac Ac
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 44, 55, 66, 77, 88, 99, 110}
= {11, 44, 55, 77, 88, 99, 110}
= {11, 22, 33, 44, 66, 77, 88, 99, 110}
Hallar:  (C△ )△B, C∩ ( −B)Ac Ac
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {20, 30, 45, 50, 55}
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
= {5, 10, 15, 25, 30, 35, 40, 45, 55, 60}
Hallar:  (A− )∩ , A∩ ( − )Cc Bc Cc Bc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 48, 56, 72, 88, 96}
= {8, 16, 24, 32, 40, 48, 72, 88, 96}
= {8, 16, 24, 32, 40, 48, 72, 80, 88, 96}
Hallar:  (C∪B)∩ , C−(B∩ )A
c Ac
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, 72, 96}
= {12, 24, 36, 48, 60, 72, 96, 108, 120}
Hallar:  (A△ )∪B, A∩ ( ∩B)Cc Cc
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 = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {8, 12, 24, 28, 32, 48}
= {8, 16, 24, 36, 40}
= {4, 12, 24, 32, 36, 40, 44, 48}
Hallar:  ( − )△ , ∩ ( ∪ )Bc Cc Ac Bc Cc Ac
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {20, 25, 30, 35, 40, 45, 50, 60}
= {5, 15, 20, 25, 40, 45, 50, 55}
= {5, 10, 30, 35, 55, 60}
Hallar:  (A− )− , A∪ ( ∪ )Bc Cc Bc Cc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {12, 18, 30, 36, 48, 54, 72}
= {6, 12, 24, 30, 36, 42, 48, 54, 60, 66, 72}
= {6, 18, 24, 30, 36, 42, 54, 66, 72}
Hallar:  ( −C)∪A, ∩ (C∪A)Bc Bc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 6, 8, 10, 12, 14, 18, 22, 24}
= {4, 6, 8, 10, 12, 14, 16, 18, 20}
= {2, 4, 6, 12, 14, 18, 24}
Hallar:  (C∪ )−A, C∩ ( ∪A)Bc Bc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 36, 45, 54, 63, 81, 90}
= {9, 18, 27, 36, 45, 54, 63, 72, 90}
= {9, 18, 27, 54, 63, 72}
Hallar:  (C∩ )∪ , C−( − )Ac Bc Ac Bc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 6, 8, 10, 14, 18, 22, 24}
= {4, 6, 8, 10, 14, 16, 18, 20, 24}
= {2, 8, 10, 12, 14, 18, 20, 22, 24}
Hallar:  ( △C)△A, −(C∩A)Bc Bc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 50, 70, 80, 90}
= {20, 30, 50, 70, 80}
Hallar:  ( −B)∩ , ∩ (B∩ )A
c 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}
= {9, 45, 54, 63, 72, 90}
= {18, 27, 36, 45, 54, 72, 81, 90}
Hallar:  (A∩ )∩B, A∩ ( ∪B)Cc Cc
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 28, 35, 42, 49, 56, 63, 70, 84}
= {14, 21, 28, 35, 49, 56, 63}
= {7, 21, 42, 49, 56, 63, 77, 84}
Hallar:  ( ∩ )△C, −( △C)Ac Bc Ac Bc
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {a, b, c, f ,h, i, j, l}
= {a, b, c, e, f , g, j,k, l}
= {a, b, d, e, f , g,h, i, j,k, l}
Hallar:  ( −C)∪A, ∪ (C∩A)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 = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {a, b, d, e, f , g,h, i, j,k, l}
= {a, b, c, d, e, f , g,h, i, j,k, l}
= {a, c, d, f , g, i, j,k}
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,h, i, l}
= {a, b, c, d, e, f , g,h, i}
= {a, c, e,h, i, j}
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, 20, 28, 32, 36, 48}
= {4, 12, 28, 32, 36, 44}
= {4, 8, 12, 16, 32, 40, 48}
Hallar:  (C− )△A, C△ ( −A)Bc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {8, 12, 16, 32, 44, 48}
= {4, 8, 24, 28, 36, 40, 44, 48}
= {8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
Hallar:( ∪A)△B, −(A△B)Cc Cc
U = {m,n, o, p, q, r, s, t,u, v,w,x}
A
B
C
= {n, o, p, q, r, s,u,w}
= {m,n, o, p, q, r, s, t,u, v,w,x}
= {n, r,u, v,x}
Hallar:  ( ∩C)∩B, △ (C∩B)Ac Ac
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 10, 15, 20, 25, 30, 35, 40, 50, 55, 60}
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
= {5, 20, 25, 30, 35, 45, 60}
Hallar:  (A∩ )△B, A△ ( ∪B)Cc Cc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 33, 55, 66, 77}
= {11, 22, 55, 77, 88, 99, 110}
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
Hallar:  ( △ )− , △ ( − )Bc Ac Cc Bc Ac Cc
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, 20, 25, 35, 55, 60}
= {10, 15, 20, 30, 45}
Hallar:  ( ∩ )− , −( ∩ )A
c Cc Bc Ac Cc Bc
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {15, 20, 25, 35, 45, 50, 55, 60}
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
= {5, 10, 25, 35, 50, 60}
Hallar:  (C∩A)△ , C△ (A∩ )Bc Bc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 60, 72, 96, 108}
= {12, 24, 36, 48, 60, 84, 96, 108, 120}
= {12, 24, 48, 72, 84, 96, 108, 120}
Hallar:  ( △ )△ , ∩ ( − )Cc Ac Bc Cc Ac Bc
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
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
= {6, 12, 24, 30, 36, 48, 60, 72}
= {6, 24, 30, 36, 42, 48, 54, 60, 66, 72}
Hallar:  (A−C)∪ , A−(C∩ )Bc Bc
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 21, 28, 42, 56, 70}
= {7, 14, 21, 28, 35, 42, 49, 63, 77}
= {7, 35, 42, 56, 70, 84}
Hallar:  (B∪A)△C, B−(A−C)
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 18, 30, 36, 66}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66}
= {6, 12, 24, 30, 42, 48, 54, 60, 66}
Hallar:  ( ∪A)∩ , ∪ (A∪ )Bc Cc Bc Cc
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 60, 80, 90, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {20, 30, 60, 70, 80, 90, 100}
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, 108, 120}
= {12, 24, 36, 48, 60, 84, 96, 108, 120}
= {12, 36, 48, 60, 72, 84, 96, 108}
Hallar:  (B∩ )∪ , B−( − )Cc Ac Cc Ac
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {18, 63, 72, 81, 90}
= {27, 45, 54, 63, 72, 81}
= {9, 18, 27, 45, 54, 63, 72, 81, 90}
Hallar:  ( ∩B)− , ∪ (B− )Ac Cc Ac Cc
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {a, b, d, e, f , g, i, j,k, l}
= {b, d, e, f , g,h, i, j,k, l}
= {a, b, d, e, f , g,h, i,k}
Hallar:  ( ∩ )− , ∩ ( − )Bc A
c Cc Bc Ac Cc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {16, 24, 32, 40, 48, 64, 80, 88}
= {8, 16, 32, 40, 48, 56, 64, 72, 80, 88, 96}
= {16, 24, 32, 56, 88, 96}
Hallar:  (B− )−C, B△ ( △C)Ac Ac
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 30, 50, 60, 70, 80}
= {10, 20, 40, 90, 100}
= {40, 50, 70, 80, 90}
Hallar:  (B−A)∩C, B−(A△C)
U = {m,n, o, p, q, r, s, t,u, v,w,x}
A
B
C
= {m,n, o, q, r, s, t, v,x}
= {n, o, p, r, t,u,w,x}
= {n, o, p, q, r, s,u, v,w}
Hallar:  ( ∩ )△C, ∪ ( △C)Bc Ac Bc Ac
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 = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {16, 24, 32, 40, 48, 64, 72}
= {16, 24, 32, 48, 72, 80, 88}
= {16, 32, 40, 56, 64, 72, 88, 96}
Hallar:  ( △ )−C, ∪ ( ∩C)Bc Ac Bc Ac
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 36, 60, 72, 120}
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 36, 48, 60, 72, 84, 96, 108}
Hallar:  ( ∩B)− , ∪ (B− )Cc A
c Cc Ac
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 48, 60, 72, 96, 108, 120}
= {12, 48, 72, 96, 108, 120}
= {48, 72, 84, 108, 120}
Hallar:  (A∪ )∩ , A∩ ( △ )Bc Cc Bc Cc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 7, 13, 17, 19, 29, 31}
= {2, 3, 5, 7, 17, 19, 23, 29, 37}
= {2, 3, 5, 17, 23, 31}
Hallar:  ( ∩B)∪ , −(B∪ )Ac Cc Ac Cc
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {b, d, f , g, i,k}
= {a, b, d, f ,h, i, j,k, l}
= {a, b, c, d, e, f , g,h, i, j,k, l}
Hallar:  ( −A)− , ∩ (A△ )Cc Bc Cc Bc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 18, 36, 45, 54, 63, 81, 90}
= {9, 18, 27, 36, 54, 63, 90}
= {9, 18, 27, 36, 45, 63, 72, 81, 90}
Hallar:  (C∩ )△A, C−( △A)Bc Bc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 72, 84, 96}
= {12, 60, 72, 84, 96, 120}
= {12, 36, 48, 60, 84}
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, 60, 80}
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 20, 30, 40, 60, 70, 90, 100}
Hallar:  (C△B)∪A, C∩ (B∪A)
U = {m,n, o, p, q, r, s, t,u, v,w,x}
A
B
C
= {n, o, p, q, r, t,u, v,w,x}
= {m,n, o, p, r, t, v}
= {n, o, p, q, r, s, t,u, v,w}
Hallar:  (A∪ )−B, A∪ ( △B)Cc Cc
U = {m,n, o, p, q, r, s, t,u, v,w,x}
A
B
C
= {m, p, q, t, v,w,x}
= {m,n, p, q, r, t,u, v,x}
= {m,n, o, p, q, r, s,u, v,w}
Hallar:  (B−A)−C, B−(A△C)
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 = {m,n, o, p, q, r, s, t,u, v,w,x}
A
B
C
= {m,n, p, r, t,u, v,w,x}
= {m,n, p, q, r, s, t,u, v,w,x}
= {m,n, o, p, v,w,x}
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, 48, 60, 72, 84, 120}
= {12, 24, 48, 72, 84, 96, 108, 120}
Hallar:  (A∩ )∩ , A∩ ( ∪ )Cc Bc Cc Bc
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 18, 24, 30, 36, 54, 66}
= {6, 24, 36, 42, 54, 72}
= {24, 30, 36, 42, 48, 54}
Hallar:  (C− )∩B, C∩ ( ∩B)Ac Ac
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}
= {24, 30, 36, 42, 48, 60, 72}
= {18, 24, 30, 60, 66, 72}
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, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 14, 42, 49, 63}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
Hallar:  ( −C)∩ , ∩ (C△ )Bc Ac Bc Ac
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {6, 9, 12, 18, 24, 27, 33, 36}
= {6, 9, 12, 18, 21, 27, 30, 33, 36}
= {9, 12, 15, 18, 21, 24, 27}
Hallar:  ( ∪ )∩ , △ ( − )Bc Cc Ac Bc Cc Ac
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {b, d, e, f , g, j,k}
= {a, b, c, d, e, f , g,h, i, j,k, l}
= {b, c, d, e, f , i}
Hallar:( − )∩A, ∩ ( △A)Cc Bc Cc Bc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {8, 20, 24, 36, 40, 44}
= {8, 12, 24, 36, 44}
= {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
Hallar:  ( △ )△ , ∩ ( ∩ )Ac Cc Bc Ac 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, 110}
= {11, 33, 55, 77, 88, 110}
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, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 8, 10, 12, 16, 18, 20, 24}
= {4, 6, 10, 14, 22, 24}
Hallar:  ( ∪B)∩ , −(B∩ )A
c Cc Ac Cc
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 = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {3, 5, 13, 19, 29, 31, 37}
= {3, 5, 19, 23, 29}
= {2, 3, 5, 7, 11, 23, 29, 31, 37}
Hallar:  ( ∩ )∪A, △ ( △A)Bc Cc Bc Cc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 12, 14, 16, 18}
= {2, 6, 12, 22, 24}
= {4, 6, 10, 14, 20, 22, 24}
Hallar:  ( ∪ )− , ∪ ( △ )Ac Bc Cc Ac Bc Cc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 18, 27, 54, 63, 72, 81, 90}
= {27, 36, 45, 54, 72, 81}
= {9, 27, 36, 45, 54}
Hallar:  (C−B)−A, C∪ (B∩A)
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 8, 12, 14, 16, 20, 24}
= {4, 6, 10, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Hallar:  (B∩A)∪ , B△ (A∪ )Cc Cc
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {10, 20, 35, 40, 45, 50, 55}
= {5, 10, 15, 20, 30, 35, 40, 50, 55, 60}
= {5, 10, 20, 35, 40, 55, 60}
Hallar:  ( ∩ )∩ , ∪ ( − )Cc 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, 36, 48, 54, 60, 66, 72}
= {12, 18, 24, 30, 42, 60, 66, 72}
= {6, 12, 18, 36, 42, 48, 60, 72}
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, 88, 99, 110}
= {11, 55, 77, 88, 99}
= {44, 55, 66, 77, 99}
Hallar:  ( ∪B)△ , ∩ (B∪ )Ac Cc Ac Cc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {18, 27, 45, 54, 63, 72, 81, 90}
= {27, 45, 63, 72, 81, 90}
= {9, 27, 36, 45, 54, 63, 72, 81, 90}
Hallar:  ( ∩B)− , −(B∪ )A
c Cc Ac Cc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 44, 55, 66, 88, 99, 110}
= {33, 44, 55, 66, 77, 88, 99}
= {11, 22, 55, 77, 99}
Hallar:  (A− )∩ , A△ ( ∪ )Cc Bc Cc 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}
= {f , g,h, i, j,k, l}
= {a, b, c, d,h, l}
Hallar:  (B∪ )∩ , B∩ ( − )A
c Cc 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 = {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, 27, 45, 54, 90}
= {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
Hallar:  ( ∪A)∪C, △ (A∪C)Bc Bc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 33, 55, 88, 99, 110}
= {11, 33, 44, 88, 99}
= {11, 44, 77, 88, 99, 110}
Hallar:  (B∪ )− , B△ ( ∪ )Ac Cc Ac Cc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 44, 55, 66, 88}
= {11, 22, 33, 55, 66, 77, 88, 99, 110}
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
Hallar:  ( ∪A)△ , ∪ (A∪ )Cc Bc Cc Bc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {24, 48, 60, 72, 120}
= {24, 36, 48, 60, 84}
= {36, 48, 60, 72, 84}
Hallar:  (C△ )∩B, C△ ( ∪B)Ac Ac
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 18, 24, 30, 48, 54, 60, 66, 72}
= {6, 18, 24, 36, 54, 66}
= {6, 18, 24, 36, 42, 48, 54, 60, 66, 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, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 3, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
Hallar:  ( ∪A)∪B, ∪ (A△B)Cc Cc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {27, 36, 54, 63, 72, 81}
= {18, 27, 36, 45, 54, 81}
= {9, 18, 27, 63, 72, 90}
Hallar:  ( ∩ )∩A, △ ( −A)Cc Bc Cc Bc
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 32, 48, 56, 64, 72, 80, 88}
= {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
= {8, 16, 24, 32, 40, 56, 64, 72, 80, 88, 96}
Hallar:  (B∩ )∩ , B∪ ( ∪ )Cc A
c Cc Ac
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {4, 14, 16, 20, 22}
= {2, 4, 8, 10, 14, 16, 18, 20, 22, 24}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Hallar:  (A∪ )∩ , A△ ( ∪ )Bc Cc Bc Cc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 44, 55, 66, 77, 88, 110}
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
= {11, 22, 33, 55, 77, 88, 99}
Hallar:  ( △B)− , −(B△ )Ac Cc Ac Cc
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 = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 32, 40, 48, 56, 64, 72, 96}
= {24, 32, 48, 56, 96}
= {8, 32, 48, 72, 96}
Hallar:  (B−A)△ , B∩ (A− )Cc Cc
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 12, 24, 28, 32, 36, 44, 48}
= {4, 8, 16, 20, 28, 32, 36, 40, 44, 48}
= {4, 8, 12, 16, 24, 28, 32, 36, 40, 44, 48}
Hallar:  ( ∩ )− , ∩ ( − )Bc A
c Cc Bc Ac Cc
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, 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, 48, 54, 60, 66, 72}
= {6, 12, 18, 30, 36, 42, 54, 60, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
Hallar:  (B∩C)−A, B△ (C△A)
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}
= {4, 8, 12, 20, 28, 32, 40, 44, 48}
= {4, 8, 16, 20, 28, 36, 40, 44, 48}
Hallar:  ( − )∪ , △ ( △ )Ac Bc Cc Ac Bc Cc
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {a, b, d, e, f , g,h, i, j,k, l}
= {a, b, d, e, f , g,h, j,k, l}
= {a, b, c,k, l}
Hallar:  ( ∩A)∩ , −(A△ )Bc Cc Bc Cc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 36, 48, 60, 72, 84, 96, 108}
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 24, 48, 96, 120}
Hallar:  (A∩C)− , A∪ (C∪ )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, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 50, 60, 70, 80, 90, 100}
Hallar:  ( ∩ )∩ , △ ( ∩ )Cc Ac Bc Cc Ac Bc
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {a, c, d, e, f , g, i, j,k, l}
= {a, b, c, d, e, f , g,h, i, j,k, l}
= {a,f , g,h, j, l}
Hallar:  ( ∩ )∪C, ∪ ( ∪C)Bc A
c Bc Ac
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {14, 21, 42, 49, 56, 63, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 14, 28, 35, 49, 56, 70, 84}
Hallar:  ( − )∪B, ∩ ( ∩B)Cc A
c Cc Ac
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,n, o, p, q, r, s, t, v,w,x}
= {n, o, q, r,u, v,w}
= {n, p, q, r, s, t,u, v,w}
Hallar:  ( − )△C, ∩ ( △C)Ac Bc Ac Bc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {3, 5, 11, 13, 23, 29}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {3, 19, 23, 29, 31, 37}
Hallar:  (A∩C)−B, A−(C−B)
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 48, 72, 84, 108}
= {24, 36, 48, 60, 72, 96, 108, 120}
= {12, 24, 36, 48, 60, 72, 84, 96, 108}
Hallar:  (A∩B)△C, A∩ (B∪C)
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {b, c, e, i, j,k, l}
= {a, b, i, j,k}
= {a, b, c, d, e, f , g,h, i, j,k, l}
Hallar:  (B△C)− , B∩ (C△ )Ac Ac
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 40, 48, 64, 80, 96}
= {16, 40, 64, 72, 80, 88}
= {32, 40, 56, 80, 88}
Hallar:  ( ∩A)△C, △ (A∪C)Bc Bc
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {c, e, g,h, j,k}
= {a, c, d, e, f , g,h, i, j}
= {d, i, j,k, l}
Hallar:  ( ∪ )∪B, −( ∪B)Ac Cc Ac Cc
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {10, 15, 20, 40, 50, 60}
= {5, 10, 15, 20, 25, 35, 45, 50, 55, 60}
= {10, 15, 40, 45, 50, 55, 60}
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, 31, 37}
= {3, 7, 17, 29, 31, 37}
= {2, 3, 5, 11, 13, 17, 19, 23, 29, 37}
Hallar:  ( ∪ )∩ , ∪ ( ∪ )Bc A
c Cc Bc Ac Cc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 12, 14, 16, 18}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 22, 24}
Hallar:  ( △ )∩ , ∩ ( △ )Ac Bc Cc Ac Bc Cc
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 15, 30, 50, 60}
= {10, 15, 20, 25, 30, 35, 45, 50, 55, 60}
= {5, 10, 35, 40, 55, 60}
Hallar:  ( − )△ , −( ∩ )Ac Cc Bc Ac 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 = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 18, 24, 30, 36, 42, 48, 54, 60, 72}
= {12, 18, 24, 42, 54, 60, 66}
= {6, 12, 18, 24, 42, 48, 72}
Hallar:  ( ∩ )−A, △ ( ∪A)Cc Bc Cc Bc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {7, 11, 13, 17, 19, 23, 29, 37}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
Hallar:  (B− )∩A, B∪ ( ∩A)Cc Cc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {24, 36, 60, 72, 96, 108, 120}
= {12, 24, 36, 48, 60, 84, 96, 108}
= {12, 24, 36, 48, 60, 96, 108, 120}
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, f , g,h, i,k, l}
= {c, e, f , g, i, j,k, l}
= {a, b, c, d, e, f , g,h, i, j,k, l}
Hallar:  ( ∩ )−A, ∪ ( ∪A)Bc Cc Bc Cc
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {36, 48, 60, 72, 84, 96, 108, 120}
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
Hallar:  (C∩A)− , C∩ (A− )Bc 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, 66, 72}
= {12, 18, 24, 36, 42, 48, 54, 72}
= {6, 18, 24, 42, 48, 66, 72}
Hallar:  (A− )∪ , A−( − )Cc Bc Cc Bc
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 18, 27, 45, 54, 81}
= {18, 27, 45, 72, 81, 90}
= {9, 36, 45, 72, 81, 90}
Hallar:  ( ∪ )∪C, ∩ ( ∩C)A
c Bc Ac Bc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 44, 66, 77, 99, 110}
= {11, 44, 55, 99, 110}
= {11, 22, 33, 44, 55, 66, 77, 88, 110}
Hallar:  ( ∩A)−C, △ (A△C)Bc Bc
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, 15, 18, 27, 33, 36}
= {3, 9, 18, 21, 27, 30, 36}
Hallar:  ( −C)∩ , △ (C△ )Ac Bc Ac Bc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {6, 8, 12, 14, 24}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 16, 18, 22}
Hallar:  ( ∪ )∪B, ∪ ( −B)A
c Cc Ac 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 = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {6, 10, 14, 16, 20, 22}
= {2, 4, 6, 8, 10, 12, 14, 18, 24}
= {4, 6, 14, 16, 18, 20, 22, 24}
Hallar:  (A− )∪B, A△ ( ∪B)Cc Cc
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {3, 5, 11, 17, 19, 31, 37}
= {3, 5, 7, 11, 17, 19, 29, 37}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
Hallar:  ( △ )△ , ∪ ( △ )Ac Cc Bc Ac Cc Bc
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {6, 12, 18, 20, 22}
= {4, 6, 10, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Hallar:  (B∪ )∩C, B△ ( △C)Ac Ac
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 40, 48, 56, 64, 72, 80, 88, 96}
= {40, 48, 56, 64, 80, 88}
= {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
Hallar:  (C− )△ , C−( ∩ )Ac Bc Ac Bc
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {6, 9, 12, 18, 21, 24, 30, 36}
= {3, 6, 12, 21, 33}
= {3, 6, 9, 12, 18, 21, 27, 30, 36}
Hallar:  (B△A)∩C, B−(A△C)
U = {m,n, o, p, q, r, s, t,u, v,w,x}
A
B
C
= {n, o, p, t,u,x}
= {m,n, o, p, q, r,u, v,w,x}
= {m,n, o, q, r, s, t,u, v,w,x}
Hallar:  (C∩B)∪ , C△ (B∩ )Ac Ac
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 33, 44, 66, 77, 88, 99, 110}
= {11, 44, 55, 66, 88}
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
Hallar:  ( −C)∩B, ∩ (C∩B)A
c Ac
U = {m,n, o, p, q, r, s, t,u, v,w,x}
A
B
C
= {m,n, o, p, q, r, t,u,w}
= {m, p, q, r, t,u,w,x}
= {m, o, p, q, r, s, t,u, v,x}
Hallar:  ( − )△ , ∩ ( △ )Bc Cc Ac Bc Cc Ac
U = {m,n, o, p, q, r, s, t,u, v,w,x}
A
B
C
= {n, o, q, r, s, t,u, v,w}
= {m, o, p, s, t,u, v,x}
= {p, q, s, t,u, v,x}
Hallar:  ( ∪ )△C, △ ( ∩C)Bc Ac Bc Ac
U = {m,n, o, p, q, r, s, t,u, v,w,x}
A
B
C
= {q, t,u,w,x}
= {m, 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
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 = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 37}
= {3, 11, 17, 19, 23, 29, 31, 37}
= {5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
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, 70, 80, 100}
= {10, 20, 40, 50, 60, 70, 80, 90, 100}
= {30, 40, 60, 70, 90}
Hallar:  (B∩C)△A, B∩ (C∪A)
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 18, 27, 36, 54, 63, 81}
= {9, 18, 36, 45, 63, 81, 90}
= {9, 27, 54, 63, 72, 90}
Hallar:  ( ∩ )△ , △ ( ∪ )Ac Cc Bc Ac Cc Bc
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 44, 77, 88, 110}
= {11, 33, 44, 66, 77, 88}
= {11, 22, 33, 44, 55, 66, 88, 99, 110}
Hallar:  ( −C)∩B, △ (C−B)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, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {14, 21, 28, 35, 49, 63, 77, 84}
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, 18, 24, 30, 36, 42, 48, 60, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 60, 66, 72}
= {12, 18, 24, 30, 36, 42, 48, 66, 72}
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, 24, 28, 32, 36, 40, 44, 48}
= {8, 20, 24, 28, 32, 36, 44, 48}
= {8, 32, 40, 44, 48}
Hallar:  ( △ )∪ , △ ( ∪ )Cc Bc Ac Cc Bc Ac
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}
= {c, f , g,h,k}
= {a, c, d, e, f , g,h, i, j,k, l}
Hallar:  (A−B)∪C, A∪ (B∩C)
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 12, 20, 28, 36}
= {4, 12, 16, 20, 24, 28, 32, 36, 40, 44}
= {4, 8, 16, 24, 28, 36, 40, 44}
Hallar:  (A∪B)△C, A△ (B∩C)
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 90}
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
Hallar:  (B∪ )∩ , B∩ ( ∪ )A
c Cc Ac Cc
HOJA DE RESPUESTAS
Operaciones entre conjuntos
Resolver las operaciones indicadas:
1). Dado el conjunto universal:
y los subconjuntos:
Hallar:
2). Dado el conjunto universal:
y los subconjuntos:
Hallar:
3). Dado el conjunto universal:
y los subconjuntos:
Hallar:
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, 37}
= {2, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
( ∩ )∩ACc Bc
Cc
Bc
∩Cc Bc
( ∩ )∩ACc Bc
△ ( −A)Cc Bc
−ABc
△ ( −A)Cc Bc
:
= {}
= {3}
= {}
= {}
:
= {}
= {}
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {a, d, e, g,h, i}
= {a, b, c, e,h, i,k, l}
= {c, d, e, f , g,h, i, j,k}
(A∪C)△Bc
Bc
A∪C
(A∪C)△Bc
A−(C∪ )Bc
C∪Bc
A−(C∪ )Bc
:
= {d, f , g, j}
= {a, c, d, e, f , g,h, i, j,k}
= {a, c, e,h, i,k}
:
= {c, d, e, f , g,h, i, j,k}
= {a}
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 70, 80, 100}
= {10, 20, 30, 40, 70, 80, 90, 100}
= {10, 30, 70, 80, 90, 100}
(B∪C)−Ac
Ac
B∪C
(B∪C)−Ac
B∪ (C△ )Ac
C△Ac
B∪ (C△ )Ac
:
= {60, 90}
= {10, 20, 30, 40, 70, 80, 90, 100}
= {10, 20, 30, 40, 70, 80, 100}
:
= {10, 30, 60, 70, 80, 100}
= {10, 20, 30, 40, 60, 70, 80, 90, 100}
4). Dado el conjunto universal:
y los subconjuntos:
Hallar:
5). Dado el conjunto universal:
y los subconjuntos:
Hallar:
6). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 18, 24, 30, 42, 48, 54, 60, 66, 72}
= {6, 12, 30, 36, 54}
= {6, 12, 24, 42, 48, 54, 60, 66, 72}
( ∪A)∪BCc
Cc
∪ACc
( ∪A)∪BCc
∩ (A△B)Cc
A△B
∩ (A△B)Cc
:
= {18, 30, 36}
= {6, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
:
= {12, 18, 24, 36, 42, 48, 60, 66, 72}
= {18, 36}
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {4, 16, 20, 24, 28, 32, 40, 44}
= {4, 8, 16, 20, 24, 28, 32, 40, 44, 48}
= {4, 8, 12, 16, 20, 24, 28, 32}
(C∩B)∩A
C∩B
(C∩B)∩A
C△ (B∪A)
B∪A
C△ (B∪A)
:
= {4, 8, 16, 20, 24, 28, 32}
= {4, 16, 20, 24, 28, 32}
:
= {4, 8, 16, 20, 24, 28, 32, 40, 44, 48}
= {12, 40, 44, 48}
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {18, 27, 36, 45, 54, 63}
= {9, 27, 36, 45, 72, 81, 90}
= {9, 18, 54, 63, 72}
(C△B)△Ac
Ac
C△B
(C△B)△Ac
C△ (B− )Ac
B−Ac
C△ (B− )Ac
:
= {9, 72, 81, 90}
= {18, 27, 36, 45, 54, 63, 81, 90}
= {9, 18, 27, 36, 45, 54, 63, 72}
:
= {27, 36, 45}
= {9, 18, 27, 36, 45, 54, 63, 72}
7). Dado el conjunto universal:
y los subconjuntos:
Hallar:
8). Dado el conjunto universal:
y los subconjuntos:
Hallar:
9). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {9, 27, 36, 45, 54, 63, 72}
= {9, 18, 27, 36, 45, 63, 81, 90}
= {18, 27, 45, 63, 72, 90}
( ∩A)△Bc Cc
Bc
Cc
∩ABc
( ∩A)△Bc Cc
∪ (A∩ )Bc Cc
A∩Cc
∪ (A∩ )Bc Cc
:
= {54, 72}
= {9, 36, 54, 81}
= {54, 72}
= {9, 36, 72, 81}
:
= {9, 36, 54}
= {9, 36, 54, 72}
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {32, 40, 56, 64, 72}
= {8, 16, 32, 40, 48, 56, 64, 72, 80, 96}
= {8, 24, 40, 72, 80, 88, 96}
( △ )∪Cc Bc Ac
Cc
Bc
Ac
△Cc Bc
( △ )∪Cc Bc Ac
△ ( ∪ )Cc Bc Ac
∪Bc Ac
△ ( ∪ )Cc Bc Ac
:
= {16, 32, 48, 56, 64}
= {24, 88}
= {8, 16, 24, 48, 80, 88, 96}
= {16, 24, 32, 48, 56, 64, 88}
= {8, 16, 24, 32, 48, 56, 64, 80, 88, 96}
:
= {8, 16, 24, 48, 80, 88, 96}
= {8, 24, 32, 56, 64, 80, 88, 96}
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {20, 30, 40, 50, 60, 70, 80, 100}
= {10, 30, 60, 70, 90, 100}
= {10, 20, 30, 40, 50, 60, 80, 90, 100}
( ∩ )−ACc Bc
Cc
Bc
∩Cc Bc
( ∩ )−ACc Bc
△ ( △A)Cc Bc
△ABc
△ ( △A)Cc Bc
:
= {70}
= {20, 40, 50, 80}
= {}
= {}
:
= {30, 60, 70, 100}
= {30, 60, 100}
10). Dado el conjunto universal:
y los subconjuntos:
Hallar:
11). Dado el conjunto universal:
y los subconjuntos:
Hallar:
12). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 18, 24, 36, 48, 54, 60, 66, 72}
= {6, 12, 30, 60, 72}
= {6, 12, 18, 24, 30, 42, 48, 54, 60, 66, 72}
( ∩A)−Bc Cc
Bc
Cc
∩ABc
( ∩A)−Bc Cc
∪ (A− )Bc Cc
A−Cc
∪ (A− )Bc Cc
:
= {18, 24, 36, 42, 48, 54, 66}
= {36}
= {18, 24, 36, 48, 54, 66}
= {18, 24, 48, 54, 66}
:
= {6, 18, 24, 48, 54, 60, 66, 72}
= {6, 18, 24, 36, 42, 48, 54, 60, 66, 72}
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {12, 36, 42, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
= {6, 24, 30, 36, 48}
( ∩ )△Cc Bc Ac
Cc
Bc
Ac
∩Cc Bc
( ∩ )△Cc Bc Ac
−( ∪ )Cc Bc A
c
∪Bc Ac
−( ∪ )Cc Bc Ac
:
= {12, 18, 42, 54, 60, 66, 72}
= {}
= {6, 18, 24, 30, 48, 54, 60}
= {}
= {6, 18, 24, 30, 48, 54, 60}
:
= {6, 18, 24, 30, 48, 54, 60}
= {12, 42, 66, 72}
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, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 77, 84}
(B△C)∩A
B△C
(B△C)∩A
B∪ (C∪A)
C∪A
B∪ (C∪A)
:
= {70}
= {70}
:
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
13). Dado el conjunto universal:
y los subconjuntos:
Hallar:
14). Dado el conjunto universal:
y los subconjuntos:
Hallar:
15). Dado el conjunto universal:
y los subconjuntos:
Hallar:
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}
= {e, f ,h, i,k, l}
= {a, b, c, d, e, g, i, j}
( − )−Cc A
c Bc
Cc
Ac
Bc
−Cc Ac
( − )−Cc A
c Bc
△ ( △ )Cc Ac Bc
△Ac Bc
△ ( △ )Cc Ac Bc
:
= {f ,h,k, l}
= {}
= {a, b, c, d, g, j}
= {f ,h,k, l}
= {f ,h,k, l}
:
= {a, b, c, d, g, j}
= {a, b, c, d, f , g,h,j,k, l}
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, 15, 18, 21, 24, 27, 30, 33, 36}
= {3, 6, 9, 12, 15, 27, 30, 33}
(C−B)∪A
C−B
(C−B)∪A
C△ (B−A)
B−A
C△ (B−A)
:
= {}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
:
= {}
= {3, 6, 9, 12, 15, 27, 30, 33}
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 35, 49, 70, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {14, 21, 49, 56, 77, 84}
( △C)∪BAc
Ac
△CAc
( △C)∪BAc
∪ (C△B)Ac
C△B
∪ (C△B)Ac
:
= {21, 28, 42, 56, 63}
= {14, 28, 42, 49, 63, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
:
= {7, 28, 35, 42, 63, 70}
= {7, 21, 28, 35, 42, 56, 63, 70}
16). Dado el conjunto universal:
y los subconjuntos:
Hallar:
17). Dado el conjunto universal:
y los subconjuntos:
Hallar:
18). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {14, 28, 42, 63, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 21, 35, 63, 70, 77, 84}
( ∪B)−ACc
Cc
∪BCc
( ∪B)−ACc
∪ (B∩A)Cc
B∩A
∪ (B∩A)Cc
:
= {14, 28, 42, 49, 56}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 21, 35, 49, 56, 70, 77}
:
= {14, 28, 42, 63, 84}
= {14, 28, 42, 49, 56, 63, 84}
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 21, 28, 35, 42, 49, 56, 70, 77, 84}
= {14, 21, 28, 35, 42, 56, 63, 70, 77, 84}
= {7, 14, 21, 28, 49, 56, 63, 70, 77}
( ∩ )−Ac Bc Cc
Ac
Bc
Cc
∩Ac Bc
( ∩ )−Ac Bc Cc
−( △ )Ac Bc Cc
△Bc Cc
−( △ )Ac Bc Cc
:
= {63}
= {7, 49}
= {35, 42, 84}
= {}
= {}
:
= {7, 35, 42, 49, 84}
= {63}
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {6, 12, 21, 24, 27}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
= {6, 12, 24, 27, 30, 33, 36}
(B△ )△CAc
Ac
B△Ac
(B△ )△CAc
B∪ ( ∩C)Ac
∩CAc
B∪ ( ∩C)A
c
:
= {3, 9, 15, 18, 30, 33, 36}
= {6, 12, 21, 24, 27}
= {21, 30, 33, 36}
:
= {30, 33, 36}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
19). Dado el conjunto universal:
y los subconjuntos:
Hallar:
20). Dado el conjunto universal:
y los subconjuntos:
Hallar:
21). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {18, 30, 48, 60, 66, 72}
= {6, 24, 42, 54, 66}
= {6, 12, 18, 30, 36, 42, 48, 54, 60, 72}
(A∪B)−C
A∪B
(A∪B)−C
A∩ (B∩C)
B∩C
A∩ (B∩C)
:
= {6, 18, 24, 30, 42, 48, 54, 60, 66, 72}
= {24, 66}
:
= {6, 42, 54}
= {}
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, 18, 24, 30, 36, 42, 48, 54, 66, 72}
= {6, 24, 30, 36, 42, 48, 54, 66, 72}
(A△ )−BCc
Cc
A△Cc
(A△ )−BCc
A∪ ( ∩B)Cc
∩BCc
A∪ ( ∩B)Cc
:
= {12, 18, 60}
= {6, 24, 30, 36, 42, 48, 54, 66, 72}
= {}
:
= {18}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 24, 30, 48, 60}
= {12, 24, 30, 36, 42, 48, 54, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 54, 72}
(C∪A)∩Bc
Bc
C∪A
(C∪A)∩Bc
C∪ (A− )Bc
A−Bc
C∪ (A− )Bc
:
= {6, 18, 60}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 72}
= {6, 18, 60}
:
= {12, 24, 30, 48}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 72}
22). Dado el conjunto universal:
y los subconjuntos:
Hallar:
23). Dado el conjunto universal:
y los subconjuntos:
Hallar:
24). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 24, 36, 48, 54}
= {6, 18, 60, 66, 72}
= {6, 12, 24, 30, 36, 42, 48, 54, 60, 66, 72}
(C∩ )∩ABc
Bc
C∩Bc
(C∩ )∩ABc
C−( −A)Bc
−ABc
C−( −A)Bc
:
= {12, 24, 30, 36, 42, 48, 54}
= {12, 24, 30, 36, 42, 48, 54}
= {12, 24, 36, 48, 54}
:
= {30, 42}
= {6, 12, 24, 36, 48, 54, 60, 66, 72}
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 33, 44, 55, 77, 88, 99, 110}
= {11, 44, 55, 66, 77, 88, 99, 110}
= {33, 66, 88, 99, 110}
(A△C)∩Bc
Bc
A△C
(A△C)∩Bc
A△ (C− )Bc
C−Bc
A△ (C− )Bc
:
= {22, 33}
= {22, 44, 55, 66, 77}
= {22}
:
= {66, 88, 99, 110}
= {22, 33, 44, 55, 66, 77}
U = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
A
B
C
= {8, 12, 24, 28, 32, 36, 44}
= {4, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}
= {4, 8, 12, 16, 20, 24, 28, 32, 40, 44, 48}
( −B)−Cc Ac
Cc
Ac
−BCc
( −B)−Cc Ac
∩ (B− )Cc Ac
B−Ac
∩ (B− )Cc Ac
:
= {36}
= {4, 16, 20, 40, 48}
= {}
= {}
:
= {12, 24, 28, 32, 36, 44}
= {36}
25). Dado el conjunto universal:
y los subconjuntos:
Hallar:
26). Dado el conjunto universal:
y los subconjuntos:
Hallar:
27). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 10, 12, 16, 18, 20, 22, 24}
= {2, 4, 6, 8, 10, 12, 14, 16, 20, 22, 24}
= {4, 6, 8, 10, 12, 16, 18, 20, 22, 24}
(A− )∩CBc
Bc
A−Bc
(A− )∩CBc
A−( ∩C)Bc
∩CBc
A−( ∩C)Bc
:
= {18}
= {2, 10, 12, 16, 20, 22, 24}
= {10, 12, 16, 20, 22, 24}
:
= {18}
= {2, 10, 12, 16, 20, 22, 24}
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 32, 40, 56, 72, 80}
= {16, 24, 32, 40, 48, 72, 80, 96}
= {8, 16, 24, 32, 64, 72, 80, 88, 96}
(A∪ )△CBc
Bc
A∪Bc
(A∪ )△CBc
A−( ∩C)Bc
∩CBc
A−( ∩C)Bc
:
= {8, 56, 64, 88}
= {8, 32, 40, 56, 64, 72, 80, 88}
= {16, 24, 40, 56, 96}
:
= {8, 64, 88}
= {32, 40, 56, 72, 80}
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 4, 6, 8, 10, 14, 18, 22, 24}
= {2, 6, 8, 12, 14, 16, 18, 20, 22}
= {2, 4, 8, 10, 12, 18}
( −A)△BCc
Cc
−ACc
( −A)△BCc
∪ (A△B)Cc
A△B
∪ (A△B)Cc
:
= {6, 14, 16, 20, 22, 24}
= {16, 20}
= {2, 6, 8, 12, 14, 18, 22}
:
= {4, 10, 12, 16, 20, 24}
= {4, 6, 10, 12, 14, 16, 20, 22, 24}
28). Dado el conjunto universal:
y los subconjuntos:
Hallar:
29). Dado el conjunto universal:
y los subconjuntos:
Hallar:
30). Dado el conjunto universal:
y los subconjuntos:
Hallar:
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, 55, 66, 77, 88}
= {22, 33, 44, 55, 66, 77, 88, 99, 110}
(B∪C)∪A
B∪C
(B∪C)∪A
B∪ (C−A)
C−A
B∪ (C−A)
:
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
= {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
:
= {}
= {11, 55, 66, 77, 88}
U = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
A
B
C
= {8, 16, 24, 32, 56, 72, 80, 88, 96}
= {8, 16, 40, 48, 80, 88, 96}
= {8, 16, 24, 32, 40, 48, 56, 64, 80, 88, 96}
(C△ )∩BAc
Ac
C△Ac
(C△ )∩BAc
C−( ∪B)Ac
∪BAc
C−( ∪B)Ac
:
= {40, 48, 64}
= {8, 16, 24, 32, 56, 80, 88, 96}
= {8, 16, 80, 88, 96}
:
= {8, 16, 40, 48, 64, 80, 88, 96}
= {24, 32, 56}
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 7, 11, 13, 17, 23, 29, 31, 37}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 3, 5, 7, 11, 13, 19, 23, 29, 37}
(B−C)△A
B−C
(B−C)△A
B∩ (C−A)
C−A
B∩ (C−A)
:
= {17, 31}
= {2, 3, 5, 7, 11, 13, 23, 29, 37}
:
= {19}
= {19}
31). Dado el conjunto universal:
y los subconjuntos:
Hallar:
32). Dado el conjunto universal:
y los subconjuntos:
Hallar:
33). Dado el conjunto universal:
y los subconjuntos:
Hallar:
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, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
( ∩A)−BCc
Cc
∩ACc
( ∩A)−BCc
∩ (A∪B)Cc
A∪B
∩ (A∪B)Cc
:
= {}
= {}
= {}
:
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
= {}
U = {m,n, o, p, q, r, s, t,u, v,w,x}
A
B
C
= {m,n, o, p, r, s, t,u, v,w}
= {m,n, o, p, q, r, t,u,x}
= {o, p, q, s,u, v,x}
( ∪ )∪Cc Bc Ac
Cc
Bc
Ac
∪Cc Bc
( ∪ )∪Cc Bc Ac
∪ ( △ )Cc Bc Ac
△Bc Ac
∪ ( △ )Cc Bc Ac
:
= {m,n, r, t,w}
= {s, v,w}
= {q,x}
= {m,n, r, s, t, v,w}
= {m,n, q, r, s, t, v,w,x}
:
= {q, s, v,w,x}
= {m,n, q, r, s, t, v,w,x}
U = {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
A
B
C
= {5, 10, 20, 25, 55, 60}
= {5, 10, 15, 20, 40, 45, 50, 55, 60}
= {15, 25, 40, 45, 50}( △A)∪Cc Bc
Cc
Bc
△ACc
( △A)∪Cc Bc
∪ (A∩ )Cc Bc
A∩Bc
∪ (A∩ )Cc Bc
:
= {5, 10, 20, 30, 35, 55, 60}
= {25, 30, 35}
= {25, 30, 35}
= {25, 30, 35}
:
= {25}
= {5, 10, 20, 25, 30, 35, 55, 60}
34). Dado el conjunto universal:
y los subconjuntos:
Hallar:
35). Dado el conjunto universal:
y los subconjuntos:
Hallar:
36). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 42, 49, 56, 70, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 84}
= {14, 21, 28, 56, 70, 84}
(C∩ )−ABc
Bc
C∩Bc
(C∩ )−ABc
C−( ∩A)Bc
∩ABc
C−( ∩A)Bc
:
= {77}
= {}
= {}
:
= {77}
= {14, 21, 28, 56, 70, 84}
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}
= {n, r, s, t,u, v,w}
( −B)∪ACc
Cc
−BCc
( −B)∪ACc
−(B△A)Cc
B△A
−(B△A)Cc
:
= {m, o, p, q,x}
= {}
= {m,n, o, p, q, r, s, t,u, v,w,x}
:
= {u}
= {m, o, p, q,x}
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, 12, 16, 20, 32, 40, 44, 48}
= {16, 24, 28, 32, 48}
( ∪ )∩CAc Bc
Ac
Bc
∪A
c Bc
( ∪ )∩CAc Bc
△ ( −C)Ac Bc
−CBc
△ ( −C)Ac Bc
:
= {}
= {8, 24, 28, 36}
= {8, 24, 28, 36}
= {24, 28}
:
= {8, 36}
= {8, 36}
37). Dado el conjunto universal:
y los subconjuntos:
Hallar:
38). Dado el conjunto universal:
y los subconjuntos:
Hallar:
39). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 30, 40, 50, 60, 90}
= {10, 30, 40, 50, 70, 80, 100}
= {10, 40, 60, 70, 90}
(C− )∪BA
c
Ac
C−Ac
(C− )∪BAc
C∪ ( −B)Ac
−BA
c
C∪ ( −B)A
c
:
= {20, 70, 80, 100}
= {10, 40, 60, 90}
= {10, 30, 40, 50, 60, 70, 80, 90, 100}
:
= {20}
= {10, 20, 40, 60, 70, 90}
U = {m,n, o, p, q, r, s, t,u, v,w,x}
A
B
C
= {m,n, o, p, q, r, s,u, v,w,x}
= {m, o, p, q, r, s, t,u, v,x}
= {n, o, p, q, t, v,x}
( − )∪Ac Cc Bc
Ac
Cc
Bc
−Ac Cc
( − )∪Ac Cc Bc
△ ( ∪ )Ac Cc Bc
∪Cc Bc
△ ( ∪ )Ac Cc Bc
:
= {t}
= {m, r, s,u,w}
= {n,w}
= {t}
= {n, t,w}
:
= {m,n, r, s,u,w}
= {m,n, r, s, t,u,w}
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {a, b, c, d, e, j,k, l}
= {a, d, e, g,h, l}
= {a, b, c, d, f , g, i, j, l}
( ∩ )∪Cc Ac Bc
Cc
Ac
Bc
∩Cc Ac
( ∩ )∪Cc Ac Bc
∪ ( − )Cc A
c Bc
−A
c Bc
∪ ( − )Cc Ac Bc
:
= {e,h,k}
= {f , g,h, i}
= {b, c, f , i, j,k}
= {h}
= {b, c, f ,h, i, j,k}
:
= {g,h}
= {e, g,h,k}
40). Dado el conjunto universal:
y los subconjuntos:
Hallar:
41). Dado el conjunto universal:
y los subconjuntos:
Hallar:
42). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {8, 12, 14, 16, 22}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 8, 12, 14, 16, 18, 20, 24}
(A△ )∪Cc Bc
Cc
Bc
A△Cc
(A△ )∪Cc Bc
A∩ ( − )Cc Bc
−Cc Bc
A∩ ( − )Cc Bc
:
= {6, 10, 22}
= {}
= {6, 8, 10, 12, 14, 16}
= {6, 8, 10, 12, 14, 16}
:
= {6, 10, 22}
= {22}
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 50, 60, 70, 80, 90, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 100}
= {10, 20, 30, 70, 90}
(B∪A)−Cc
Cc
B∪A
(B∪A)−Cc
B−(A∩ )Cc
A∩Cc
B−(A∩ )Cc
:
= {40, 50, 60, 80, 100}
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {10, 20, 30, 70, 90}
:
= {50, 60, 80, 100}
= {10, 20, 30, 40, 70}
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {6, 9, 12, 15, 21, 27, 33, 36}
= {6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
= {6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
( ∪A)△BCc
Cc
∪ACc
( ∪A)△BCc
∩ (A−B)Cc
A−B
∩ (A−B)Cc
:
= {3}
= {3, 6, 9, 12, 15, 21, 27, 33, 36}
= {3, 18, 24, 30}
:
= {}
= {}
43). Dado el conjunto universal:
y los subconjuntos:
Hallar:
44). Dado el conjunto universal:
y los subconjuntos:
Hallar:
45). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 30, 40, 50, 70, 80, 90, 100}
= {10, 20, 30, 60, 80}
= {10, 20, 30, 40, 60, 70, 80, 90, 100}
(A∪ )∩BCc
Cc
A∪Cc
(A∪ )∩BCc
A∪ ( −B)Cc
−BCc
A∪ ( −B)Cc
:
= {50}
= {10, 20, 30, 40, 50, 70, 80, 90, 100}
= {10, 20, 30, 80}
:
= {50}
= {10, 20, 30, 40, 50, 70, 80, 90, 100}
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 36, 48, 60, 84, 108}
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
= {24, 36, 48, 60, 72, 84, 108}
( ∩A)∩Cc Bc
Cc
Bc
∩ACc
( ∩A)∩Cc Bc
−(A− )Cc Bc
A−Bc
−(A− )Cc Bc
:
= {12, 96, 120}
= {}
= {12}
= {}
:
= {12, 24, 36, 48, 60, 84, 108}
= {96, 120}
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 33, 44, 66, 77, 88, 110}
= {33, 55, 66, 77, 88, 110}
= {44, 55, 66, 77, 88, 110}
(C△A)∩Bc
Bc
C△A
(C△A)∩Bc
C∩ (A− )Bc
A−Bc
C∩ (A− )Bc
:
= {11, 22, 44, 99}
= {11, 22, 33, 55}
= {11, 22}
:
= {33, 66, 77, 88, 110}
= {66, 77, 88, 110}
46). Dado el conjunto universal:
y los subconjuntos:
Hallar:
47). Dado el conjunto universal:
y los subconjuntos:
Hallar:
48). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {9, 18, 27, 36, 45, 54, 63, 72, 81, 90}
A
B
C
= {18, 27, 36, 45, 63, 72, 81, 90}
= {18, 27, 45, 72, 81}
= {9, 18, 36, 45, 72, 90}
( − )△Cc Ac Bc
Cc
Ac
Bc
−Cc Ac
( − )△Cc Ac Bc
∪ ( − )Cc A
c Bc
−Ac Bc
∪ ( − )Cc Ac Bc
:
= {27, 54, 63, 81}
= {9, 54}
= {9, 36, 54, 63, 90}
= {27, 63, 81}
= {9, 27, 36, 54, 81, 90}
:
= {}
= {27, 54, 63, 81}
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, b, c, d, e,h, i,k}
= {a, b, e, f , g, i, j,k, l}
( − )△Bc Ac Cc
Bc
Ac
Cc
−Bc Ac
( − )△Bc Ac Cc
∩ ( △ )Bc Ac Cc
△Ac Cc
∩ ( △ )Bc Ac Cc
:
= {f , g, j, l}
= {a, f , l}
= {c, d,h}
= {g, j}
= {c, d, g,h, j}
:
= {a, c, d, f ,h, l}
= {f , l}
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 28, 42, 56, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 70, 77, 84}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 84}
( − )△CBc Ac
Bc
Ac
−Bc Ac
( − )△CBc Ac
−( −C)Bc A
c
−CAc
−( −C)Bc Ac
:
= {63}
= {21, 35, 49, 63, 70, 77}
= {}
= {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 84}
:
= {77}
= {63}
49). Dado el conjunto universal:
y los subconjuntos:
Hallar:
50). Dado el conjunto universal:
y los subconjuntos:
Hallar:
51). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
A
B
C
= {12, 24, 48, 60, 84, 96, 108, 120}
= {12, 24, 48, 60, 72, 84, 96, 108, 120}
= {12, 24, 36, 48, 60, 72, 84, 96, 108, 120}
( ∪ )∩BA
c Cc
Ac
Cc
∪Ac Cc
( ∪ )∩BAc Cc
△ ( −B)Ac Cc
−BCc
△ ( −B)Ac Cc
:
= {36, 72}
= {}
= {36, 72}
= {72}
:
= {}
= {36, 72}
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {11, 22, 44, 55, 66, 77, 88, 99}
= {11, 22, 33, 44, 55, 66, 99, 110}
= {11, 22, 33, 44, 88}
(C△A)∩B
C△A
(C△A)∩B
C△ (A△B)
A△B
C△ (A△B)
:
= {33, 55, 66, 77, 99}
= {33, 55, 66, 99}
:
= {33, 77, 88, 110}
= {11, 22, 44, 77, 110}
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {10, 20, 60, 70, 80}
= {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
= {30, 40, 50, 60, 80, 100}
( ∩A)−BCc
Cc
∩ACc
( ∩A)−BCc
△ (A∩B)Cc
A∩B
△ (A∩B)Cc
:
= {10, 20, 70, 90}
= {10, 20, 70}
= {}
:
= {10, 20, 60, 70, 80}
= {60, 80, 90}
52). Dado el conjunto universal:
y los subconjuntos:
Hallar:
53). Dado el conjunto universal:
y los subconjuntos:
Hallar:
54). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {11, 22, 33, 44, 55, 66, 77, 88, 99, 110}
A
B
C
= {22, 33, 44, 66, 88}
= {22, 33, 44, 55, 66, 99}
= {11, 22, 33, 44, 55, 66, 110}
(A− )∩CBc
Bc
A−Bc
(A− )∩CBc
A△ ( ∩C)Bc
∩CBc
A△ ( ∩C)Bc
:
= {11, 77, 88, 110}
= {22, 33, 44, 66}
= {22, 33, 44, 66}
:
= {11, 110}
= {11, 22, 33, 44, 66, 88, 110}
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 9, 15, 18, 21, 24, 27, 30, 33, 36}
= {15, 18, 24, 27, 30, 36}
= {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
( − )∩Bc Cc Ac
Bc
Cc
Ac
−Bc Cc
( − )∩Bc Cc Ac
−( − )Bc Cc Ac−Cc A
c
−( − )Bc Cc Ac
:
= {3, 6, 9, 12, 21, 33}
= {}
= {6, 12}
= {3, 6, 9, 12, 21, 33}
= {6, 12}
:
= {}
= {3, 6, 9, 12, 21, 33}
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, 32, 40, 64, 72, 88, 96}
= {16, 24, 40, 56, 64, 72, 80, 88, 96}
( ∪A)−BCc
Cc
∪ACc
( ∪A)−BCc
∩ (A∪B)Cc
A∪B
∩ (A∪B)Cc
:
= {8, 32, 48}
= {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
= {24, 48, 56, 80}
:
= {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
= {8, 32, 48}
55). Dado el conjunto universal:
y los subconjuntos:
Hallar:
56). Dado el conjunto universal:
y los subconjuntos:
Hallar:
57). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {a, g,h, i, l}
= {a, c, d, e, f ,h, i, j,k, l}
= {a, b, c, d, e, f , g,h, i, j,k, l}
(C△B)−A
C△B
(C△B)−A
C△ (B△A)
B△A
C△ (B△A)
:
= {b, g}
= {b}
:
= {c, d, e, f , g, j,k}
= {a, b,h, i, l}
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {b, e, f , i, j,k}
= {a, d, e, f , g,h, i, j,k, l}
= {a, b, f , g, i, j,k, l}
(B− )−Ac Cc
Ac
Cc
B−A
c
(B− )−Ac Cc
B∪ ( − )Ac Cc
−Ac Cc
B∪ ( − )Ac Cc
:
= {a, c, d, g,h, l}
= {c, d, e,h}
= {e, f , i, j,k}
= {f , i, j,k}
:
= {a, g, l}
= {a, d, e, f , g,h, i, j,k, l}
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}
= {5, 10, 15, 25, 40, 45, 60}
= {5, 10, 15, 20, 25, 35, 40, 45, 50, 60}
(B∩A)−C
B∩A
(B∩A)−C
B∩ (A△C)
A△C
B∩ (A△C)
:
= {5, 10, 15, 25, 40, 45}
= {}
:
= {30, 55, 60}
= {60}
58). Dado el conjunto universal:
y los subconjuntos:
Hallar:
59). Dado el conjunto universal:
y los subconjuntos:
Hallar:
60). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {14, 28, 35, 42, 56, 63, 70, 77, 84}
= {7, 14, 21, 28, 49, 63, 70, 84}
= {7, 14, 21, 28, 35, 56, 63, 77, 84}
(C−A)−Bc
Bc
C−A
(C−A)−Bc
C∪ (A△ )Bc
A△Bc
C∪ (A△ )Bc
:
= {35, 42, 56, 77}
= {7, 21}
= {7, 21}
:
= {14, 28, 63, 70, 84}
= {7, 14, 21, 28, 35, 56, 63, 70, 77, 84}
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}
= {3, 6, 15, 18, 21, 24, 27, 30}
( − )∪CBc Ac
Bc
Ac
−Bc Ac
( − )∪CBc Ac
△ ( −C)Bc Ac
−CAc
△ ( −C)Bc Ac
:
= {15, 21}
= {}
= {15, 21}
= {3, 6, 15, 18, 21, 24, 27, 30}
:
= {}
= {15, 21}
U = {a, b, c, d, e, f , g,h, i, j,k, l}
A
B
C
= {b, f , g, i, j, l}
= {a, d, e,h, i, j,k, l}
= {b, d, e, f , g,h, j,k}
(B∪ )−ACc
Cc
B∪Cc
(B∪ )−ACc
B−( ∪A)Cc
∪ACc
B−( ∪A)Cc
:
= {a, c, i, l}
= {a, c, d, e,h, i, j,k, l}
= {a, c, d, e,h,k}
:
= {a, b, c, f , g, i, j, l}
= {d, e,h,k}
61). Dado el conjunto universal:
y los subconjuntos:
Hallar:
62). Dado el conjunto universal:
y los subconjuntos:
Hallar:
63). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 18, 24, 30, 36, 54, 60, 66, 72}
= {6, 12, 18, 30, 36, 42, 60, 66, 72}
= {6, 24, 36, 42, 54, 72}
( ∪ )△Cc Bc Ac
Cc
Bc
Ac
∪Cc Bc
( ∪ )△Cc Bc Ac
△ ( ∪ )Cc Bc Ac
∪Bc Ac
△ ( ∪ )Cc Bc Ac
:
= {12, 18, 30, 48, 60, 66}
= {24, 48, 54}
= {42, 48}
= {12, 18, 24, 30, 48, 54, 60, 66}
= {12, 18, 24, 30, 42, 54, 60, 66}
:
= {24, 42, 48, 54}
= {12, 18, 24, 30, 42, 54, 60, 66}
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, 10, 25, 30, 40, 45}
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
(C∩ )−ABc
Bc
C∩Bc
(C∩ )−ABc
C∪ ( △A)Bc
△ABc
C∪ ( △A)Bc
:
= {15, 20, 35, 50, 55, 60}
= {15, 20, 35, 50, 55, 60}
= {}
:
= {5, 10, 25, 30, 40, 45}
= {5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60}
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}
= {6, 12, 18, 24, 36, 48, 54, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
(B∪ )△CAc
Ac
B∪Ac
(B∪ )△CAc
B△ ( ∩C)Ac
∩CAc
B△ ( ∩C)Ac
:
= {72}
= {6, 12, 18, 24, 36, 48, 54, 66, 72}
= {30, 42, 60}
:
= {72}
= {6, 12, 18, 24, 36, 48, 54, 66}
64). Dado el conjunto universal:
y los subconjuntos:
Hallar:
65). Dado el conjunto universal:
y los subconjuntos:
Hallar:
66). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
A
B
C
= {2, 3, 5, 23, 37}
= {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 7, 17, 19, 23}
(C△A)△B
C△A
(C△A)△B
C∪ (A∪B)
A∪B
C∪ (A∪B)
:
= {3, 5, 7, 17, 19, 37}
= {11, 13, 23, 29, 31}
:
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
= {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}
U = {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
A
B
C
= {6, 12, 24, 30, 48, 54, 60, 66}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
= {6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72}
(B−A)∩Cc
Cc
B−A
(B−A)∩Cc
B−(A− )Cc
A−Cc
B−(A− )Cc
:
= {}
= {18, 36, 42, 72}
= {}
:
= {6, 12, 24, 30, 48, 54, 60, 66}
= {18, 36, 42, 72}
U = {10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
A
B
C
= {20, 40, 50, 60, 70, 80, 90, 100}
= {20, 30, 40, 50, 60, 70, 80, 90, 100}
= {40, 60, 70, 90, 100}
(B△A)∩C
B△A
(B△A)∩C
B∩ (A∪C)
A∪C
B∩ (A∪C)
:
= {30}
= {}
:
= {20, 40, 50, 60, 70, 80, 90, 100}
= {20, 40, 50, 60, 70, 80, 90, 100}
67). Dado el conjunto universal:
y los subconjuntos:
Hallar:
68). Dado el conjunto universal:
y los subconjuntos:
Hallar:
69). Dado el conjunto universal:
y los subconjuntos:
Hallar:
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, 24}
= {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
= {2, 4, 6, 8, 10, 12, 14, 16, 20, 22, 24}
( △ )∩CBc Ac
Bc
Ac
△Bc Ac
( △ )∩CBc Ac
∪ ( △C)Bc Ac
△CAc
∪ ( △C)Bc Ac
:
= {}
= {8}
= {8}
= {8}
:
= {2, 4, 6, 10, 12, 14, 16, 20, 22, 24}
= {2, 4, 6, 10, 12, 14, 16, 20, 22, 24}
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}
= {a, c, d, f , g,h, i,k}
= {a, b, d, e, f , g,h, i, j, l}
( ∪ )−Cc Bc A
c
Cc
Bc
Ac
∪Cc Bc
( ∪ )−Cc Bc Ac
∪ ( △ )Cc Bc Ac
△Bc Ac
∪ ( △ )Cc Bc Ac
:
= {c,k}
= {b, e, j, l}
= {j,k, l}
= {b, c, e, j,k, l}
= {b, c, e}
:
= {b, e,k}
= {b, c, e,k}
U = {3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36}
A
B
C
= {3, 6, 9, 15, 21, 24, 27, 33, 36}
= {3, 6, 9, 18, 24, 33, 36}
= {3, 6, 9, 12, 15, 18, 21, 27, 30, 33, 36}
( ∩A)△CBc
Bc
∩ABc
( ∩A)△CBc
−(A−C)Bc
A−C
−(A−C)Bc
:
= {12, 15, 21, 27, 30}
= {15, 21, 27}
= {3, 6, 9, 12, 18, 30, 33, 36}
:
= {24}
= {12, 15, 21, 27, 30}
70). Dado el conjunto universal:
y los subconjuntos:
Hallar:
71). Dado el conjunto universal:
y los subconjuntos:
Hallar:
72). Dado el conjunto universal:
y los subconjuntos:
Hallar:
U = {7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84}
A
B
C
= {7, 14, 21, 35, 42, 49, 56, 63, 70, 77, 84}
= {7, 21, 35, 42, 49, 63, 70, 77, 84}
= {14, 21, 28, 35, 56, 63, 70, 77, 84}
( ∪B)−Cc A
c
Cc
Ac
∪BCc
( ∪B)−Cc Ac
∩ (B− )Cc A
c
B−A
c
∩ (B− )Cc Ac
:
= {7, 42, 49}
= {28}
= {7, 21, 35, 42, 49, 63, 70, 77, 84}
= {7, 21, 35, 42, 49, 63, 70, 77, 84}
:
= {7, 21, 35, 42, 49, 63, 70, 77, 84}
= {7, 42, 49}
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, 24}
= {6, 10, 14, 20, 22, 24}
= {2, 4, 12, 16, 18, 24}
( − )△CBc Ac
Bc
Ac
−Bc Ac
( − )△CBc Ac
∩ ( ∪C)Bc Ac
∪CA
c
∩ ( ∪C)Bc Ac
:
= {2, 4, 8, 12, 16, 18}
= {22}
= {2, 4, 8, 12, 16, 18}
= {8, 24}
:
= {2, 4, 12, 16, 18, 22, 24}
= {2, 4, 12, 16, 18}
U = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
A
B
C
= {2, 4, 6, 8, 12, 14, 16, 20}
= {2, 8, 14, 22, 24}
= {2, 6, 10, 14, 16, 18, 20, 22}
( ∪ )∩ACc Bc
Cc
Bc
∪Cc Bc
( ∪ )∩ACc Bc
△ ( △A)Cc Bc
△ABc
△ ( △A)Cc Bc
:
= {4, 8, 12, 24}
= {4, 6, 10, 12, 16, 18, 20}
= {4, 6, 8, 10, 12, 16, 18, 20, 24}
= {4, 6, 8, 12, 16, 20}
:
= {2, 8, 10, 14, 18}
= {2, 4, 10, 12, 14,