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Question

In a class of 70 students, 38 students like physics, 21 students like mathematics and 15 students like both the subjects, then the number of students who like neither of the subjects is

A
27
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B
24
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C
11
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D
26
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Solution

The correct option is D 26
Let A and B denote the number of students who like physics and mathematics respectively.
Then n(A)=38, n(B)=21, n(AB)=15
n(AB)=n(AB)
=n(U)n(AB)
where U is the universal set.
n(AB)=70(38+2115)
=26

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n(A∪B) = n(A) + n(B) − n(A∩B)
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