# In the following question explain your reasoning, either by giving a proof of your assertion or a counterexample.

**Question: In the following question explain your reasoning, either by giving a proof of your assertion or a counterexample.**

Question: Is it true that for any two sets A and B, A ∩ B = A ∪ B implies that A = B?

Answer: Yes, it is true. To prove it, we will use the fact that A ⊆ B if and only if A ∩ B = A. First, assume that A ∩ B = A ∪ B. Then, we have that A ⊆ A ∩ B, since A is a subset of any union that contains it. But by the given assumption, we also have that A ∩ B ⊆ A, since A ∩ B is a subset of any intersection that contains it. Therefore, by the definition of set equality, we have that A = A ∩ B. Similarly, we can show that B = A ∩ B. Hence, we have that A = B, as required.

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