If n(A) = 5 and n(B) = 10 , then find maximum and minimum possible values of n(A ∩ B) if

(a) n(U) = 8

(b) n(U) = 20

Also explain the answer.

# If n(A) = 5 and n(B) = 10 , then find maximum and minimum possible values of n(A ∩ B) if

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Answer:Answer

Set A has 7 elements & set B has 8 elements.

Minimum A∪B elements condition: Out of 8 elements of set B, 7 elements are identical to that of set A. In this case A∪B=B & it will have 8 elements.

Maximum A∪B elements condition: A & B are disjoint sets, that no element will be common to them. Then:

n(A∪B)=n(A)+n(B).

A∪B has 15 elements.