设A,B,C,D是任意集合,求证:(A∩B)x(C∩D)=(AxC)∩(BxD)
问题描述:
设A,B,C,D是任意集合,求证:(A∩B)x(C∩D)=(AxC)∩(BxD)
答
求证:((A∩B)∪(C∩D)=(A∪C)∩(B∪D)for all x ∈ (A∩B)∪(C∩D)x ∈ (A∩B) or x ∈(C∩D)(x ∈ A and x ∈B )or (x ∈ C and x ∈D )(x ∈ A or x ∈C )and (x ∈ B or x ∈D )x ∈(A∪C) and x ∈ (B∪D)x ∈(...