Which of the following properties are true for the real numbers a, b, and c?
Trichotomy: If a and b are two real numbers, one and only one of the following possibilities is true: a < b or a = b or a > b.
Transitivity: a < b and b < c implies a < c.
Monotonicity of addition: a < b implies a + c < b + c.
Monotonicity of multiplication: a < b and c > 0 implies a * c < b * c.
The multiplication is commutative: a * b = b * a.
The multiplication is associative: (a * b) * c = a * (b * c).
a * 1 = 1 * a = a (1 is the neutral element for the product).
a * a^-1 = 1 (if a is different from 1) (a^-1 is the multiplicative inverse of a).
The distributive property of multiplication with respect to addition links both operations: a * (b + c) = a * b + a * c.
The opposite of the sum is the sum of the opposites: -(a + b) = -a + (-b).
The product of any real number by (-1) is equal to the opposite of the real number: a * (-1) = (-1) * a = (-a).
The product of a real number by zero is zero: a * 0 = 0 * a = 0.
If a * b = 0 then a = 0 or b = 0.
Cancellation law: of the sum: If a + c = b + c then a = b. of the product: If a * c = b * c and c is different from 0 then a = b.

a) Only the first four properties are true.
b) Only the first eight properties are true.
c) All properties are true.
d) None of the properties are true.