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Question

Let A and B be two sets containing 4 and 7 elements respectively. If the minimum and maximum number of elements in AB are m and n respectively, then m+n is

A
18
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B
19
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C
20
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D
21
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Solution

The correct option is A 18
n(AB)=n(A)+n(B)n(AB)
For maximum value of n(AB), n(AB) should be minimum, i.e., n(AB)=0
max(n(AB))=n(A)+n(B)n=4+7=11

For minimum value of n(AB), n(AB) should be maximum, i.e., n(AB)=4
min(n(AB))=n(A)+n(B)4m=4+74=7

Hence, m+n=7+11=18

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