Q4 of 162 Page 1

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

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


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