Let A and B be two sets having 3 and 6 elements respectively. Write the minimum number of elements that can have.

Question

Philoid · Accepted Answer

Here, n(A)=3 and n(B)=6

Now, n(A⋃B)=n(A)+n(B)-n(A⋂B)

=3+6-n(A⋂B)

=9-n(A⋂B)

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

Now,A⊂B then max(n(A⋂B))=n(A)=3.

∴ min(n(A⋃B) )=9-3=6