The expression X (X Y) = X Y can be shown to be valid using set identities. Specifically, the distributive property states that for any sets A, B, and C, A (B ∪ C) = (A B) ∪ (A C). Applying this to X (X Y) yields X (X Y) = (X X) ∪ (X Y) = X ∪ (X Y) = X Y, demonstrating the validity of the original expression.

1. Use set identities to show that the following expression is valid. X ( X Y ) = X Y