There are 23 people in a class, out of which 13 people like Maths and 12 people like English. If the number of people who doesn't like Maths and English is 1, find the number of people who like both Maths and English.

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Solution

The correct option is D 3

Number of elements in universal set is n(U)= 23.

Let A, B, C, D be the sets containing people who like only Maths, only English, Maths and English

And who doesn't like maths and English respectively?

People who likes Maths = n(A)+ n (C)

People who likes English = n(B) + n (C)

People who doesn't like Maths and English =n(U)- n(A)-n(B)-n(c)

n(A) + n(C) = 13

n(B) + n(C) =12

1 = 23 - n(A) -n(B) -n(C)

Solving we get n(C) =3

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