Question

Let A and B be sets. If A ∩ X = B ∩ X = φ and A ∪ X = B ∪ X for some set X then show that A = B

Answer 1

here you question saying that
A ∩ X = B ∩X = φ( empty sets )
that means it X doesn't have the element of A and B.

But when A ∪ X = B ∪ X this condition is here so, A and X have the element same as the element B and X have.