Final answer:
Sets A and C are mutually exclusive, meaning their probability of occurring together is zero. For sets A and B, they could be dependent or independent, based on whether P(A AND B) equals P(A)P(B). Algebraic rules such as commutativity apply to both numbers and set operations.
Step-by-step explanation:
Understanding Sets and Probability
When examining relationships between sets, such as A and B, it's essential to determine if sets are mutually exclusive or independent. Sets A and C are given as mutually exclusive since they have no elements in common, hence P(A AND C) = 0. This means the probability of both events A and C occurring at the same time is zero.
For sets that are not known to be mutually exclusive or independent, it is often assumed they are dependent until proven otherwise. For instance, if A and B are mutually exclusive, this would mean P(A AND B) = 0. However, if they are independent, then P(A AND B) = P(A)P(B).
Operations on sets follow specific algebraic rules, such as the commutative property where A + B = B + A, applicable to set union as well as to the addition of numbers. Understanding these relationships assists in solving problems related to set theory and probability.