Question

Let = {1,2,3,4,5,6,7,8,9,10}, = {1,2,4,7,8}, = {2,4,6,8,10}, = {3,5,6,7} then show that (i) ∩ ( ∪ ) = ( ∩ ) ∪ ( ∩ ) (ii) ( ∩ ) ′ = ′ ∪ ′​

Answer 1

Answer:

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

′