Question

If U = {1,2,3,4,……..,10} is the universal set for the sets A = {2,3,4,5} and B = {1,2,3,4,5,6}, then verify that (A∪B)'' = A''∩B''.

Answer 1

Step-by-step explanation:

Given, universal set, U={1,2,3,4,5,6,7}

A={1,2,5,7}

B={3,4,5,6}

(A∪B)

′

=U−(A∪B)

={1,2,3,4,5,6,7}−{1,2,3,4,5,6,7}

=ϕ

A

′

∩B

′

=(U−A)n(U−B)

={3,4,6}n{1,2,7}

=ϕ

Hence (A∪B)

′

=A

′

∩B

′

.

solution