By cases 1 and 2,x∈A∩B or x∈A∩C, and so, by definition of U,x∈ [So A∩(B∪C)⊆(A∩B)∪(A∩C) by definition of subset.] (2) Proof that (A∩B)∪(A∩C)⊆A∩(B∪C) : Let x∈(A∩B)∪(A∩...