Question

If Universal set = {x:x belongs to N,x less than equal to 12}, A= {x:x greater than equal to 7} and B= {x:4 less than x less than 10}, then find : A', B', AUB, A intersection B, A-B, B-A, (AUB)', A' intersection B'. Also verify that : i) (AUB)'= A' intersection B'. ii) A-B = A intersection B'. iii) n(AUB) + n((AUB)') = n(universal set). iv) n(AUB) = n(A-B)+n(B-A) + n(A intersection B)​

Answer 1

Answer:

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

′

.