Let A and B be two sets having 3 and 6 elements respectively. Write th – InterviewSolution

1.

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

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

Discussion

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