Let U = { 1, 2, 3, 4, 5, 6, 7}, A = { 2, 3, 5, 7} and B = { 2, 4, 7} . Find the set A ∩ B . A ∩ B =

Solution

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U={1,2,3,4,5,6,7,8,9}

A={1,2,3,4}

B={2,4,6,8}

C={3,4,5,6}

(i) A

′

=U−A={5,6,7,8,9}

(ii) B

′

={1,3,5,7,9}

(iii) A∪C={1,2,3,4,5,6}

∴(A∪C)

′

={7,8,9}

(iv) A∪B={1,2,3,4,6,8}

(A∪B)

′

={5,7,9}

(v) We know (A

′

)

′

=A

⇒(A

′

)

′

={1,2,3,4}

(vi) B−C={2,8}

∴(B−C)

′

={1,3,4,5,6,7,9}