Q. 35.0( 1 Vote )

# If A and B are tw

Let A and B be two sets with n(A) = 13, n(B) = 16.

We have, n(A B) = n(A) + n(B) – n(A B)

Minimum number of elements in A B is possible if all the elements of A lie in B, i.e. A B (B cannot be a subset of A, obviously, as n(B) > n(A)).

In that case, n(A B) = n(A) + n(B) – n(A B)

n(A B) = 13 + 16 – 13 = 16

Maximum number of elements in A B is possible if n(A B) = 0,

i.e. if A and B are disjoint sets.

In that case, n(A B) = n(A) + n(B) – n(A B)

n(A B) = 13 + 16 – 0 = 29

So, minimum and maximum number of elements possible in A B are 16 and 29 respectively.

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