Let A and B be two sets having 4 and 7 elements respectively. Then write the maximum number of elements that can be.

Question

Philoid · Accepted Answer

Here, n(A)=4 and n(B)=7

Now, n(A⋃B) =n(A)+n(B)-n(A⋂B)

=4+7-n(A⋂B)

=11-n(A⋂B)

So, n(A⋃B) is maximum whenever n(A⋂B) is minimum and it is possible only when A⋂B=ϕ

Now, A⋂B=ϕ then min(n(A⋂B)) =0.

∴ min(n(A⋃B))=11-0=11