Final answer:
The statement A ∪ (A ∩ B) = A is always true, as it represents the absorption law in set theory, which implies no new elements are added to set A by uniting it with the intersection of A and B.
Step-by-step explanation:
The question is asking whether the statement A ∪ (A ∩ B) = A is always true, sometimes true, or always false. This statement is a law of set theory known as the absorption law, which states that for any sets A and B, the union of set A with the intersection of set A and set B is equal to set A. This is because the intersection of A and B (A ∩ B) will result in a set of elements that are in both A and B, and when we take the union of A and this intersection, we are not adding any new elements to set A that weren't already there. Thus, the outcome is simply set A. Therefore, the correct answer is A: Always true.
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