Final answer:
The statement (A∩B) = A′∪B′ is not always true. It is true only when A and B are mutually exclusive.
Step-by-step explanation:
The given statement (A∩B) = A′∪B′ can be rephrased as the intersection of sets A and B is equal to the union of their complements. To decide whether this statement is always true or not always true, we need to consider whether A and B are mutually exclusive or not.
If A and B are mutually exclusive, it means that the sets have no elements in common. In this case, (A∩B) will be an empty set, and the statement will be true. On the other hand, if A and B are not mutually exclusive, there will be some elements that are common to both sets, and the statement will be false.
Therefore, the statement (A∩B) = A′∪B′ is not always true. It is true only when A and B are mutually exclusive.