Q7 of 162 Page 1

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

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


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