# Proof:A ∩ (B∪C) ⊆ (A∩B) ∪ (A∩C)

Proof:
Choose arbitrary sets , , and . We want to show to show that every is also in . Choose an arbitrary in the left hand side. Then and . This means either (1) or (2) . In case (1), we have and , so , and thus . Case (2) is similar. In either case, , as required.