Let A = {2, 4, 6, 8, 10}, B = {4, 8, 12, 16} and C = {6, 12, 18, 24}.

Using Venn diagrams, verify that:


(i) (A ∪ B) ∪ C = A ∪ (B ∪ C)


(ii) (A ∩ B) ∩ C = A ∩ (B ∩ C).


(i) LHS:


AB = {2, 4, 6, 8, 10, 12, 16} (AB)C = {2, 4, 6, 8, 10, 12, 16, 18, 24}


A


B


RHS:


BC = {4, 6, 8, 10, 12, 16, 18, 24}


BC


A(BC) = {2, 4, 6, 8, 10, 12, 16, 18, 24}



LHS = RHS. [Verified]


(ii)LHS:


AB = {4, 8} (AB)C = {} or ø


A


B


RHS:


BC = {12} A(BC) = {}



LHS = RHS.[Verified]


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