Question

In a class of $60$ students, $25$ students play cricket and $20$ students play tennis, and $10$ students play both the games, then the number of students who play neither are

• A. $0$
• B. $35$
• C. $45$
• D. $25$

Answer 1

The correct option is D $25$

Let 'A' be the set of students who play cricket, 'B' be the set of students who play tennis.

It is given that, $n\left(A\right)=25$, $n\left(B\right)=20$ and $n(A\cap B)=10=$ students who play both the games

Thus $n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)=20+25-10=35$

Therefore the students who play neither of the cricket and tennis $=60-35=25$