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Class 11

>>Maths

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>>Complement of Sets

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

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If U={1,2,3,4,5,6,7,8,9},A={2,4,6,8} and B={2,3,5,7}. Verify that

(i) (A∪B)

′

=A

′

∩B

′

(ii) (A∩B)

′

=A

′

∪B

′

Medium

Solution

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

A={2,4,6,8}

B={2,3,5,7}

(i) (A∪B)

′

={2,3,4,5,6,7,8}

′

={1,9}

A

′

∩B

′

={1,3,5,7,9}∩{1,4,6,8,9}={1,9}

∴(A∪B)

′

=A

′

∩B

′

(ii) (A∩B)

′

={2}

′

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

A

′

∪B

′

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

∴(A∩B)

′

=A

′

∪B