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

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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