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]