



 
Hello Gloria, If A = X and B = X, then A ∩ B = X ∩ X = X. Thus we have, A = X and B = X ⇒ A ∩ B = X. If A ∩ B = X, then we have that X ∩ A, and X ⊆ B, which is only part of what we need to solve the converse. We require more information, since in general a counterexample can be found.For instance, if A = { 1, 2, 3 } and B = { 2, 3, 4 }, then X = A ∩ B = { 2, 3 } and clearly A ≠ X, B ≠ X. Tyler  


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