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In a class of 60 students, 25 students play cricket and 20 students play tennis and 10 students play both the games. Find the number of students who play neither.
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Verified Answer
Let $C$ be the set of students who play cricket and $T$ be the set of students who play tennis. Then, $n(U)=60$, $n(C)=25, n(T)=20$,
and $n(C \cap T)=10$
We have $n(C \cup T)=n(C)+n(T)-n(C \cup T)$
$$
=25+20-10=35
$$
So, Number of students who play neither $=n(U)-n(C \cup \mathrm{T})=60-35=25$
and $n(C \cap T)=10$
We have $n(C \cup T)=n(C)+n(T)-n(C \cup T)$
$$
=25+20-10=35
$$
So, Number of students who play neither $=n(U)-n(C \cup \mathrm{T})=60-35=25$
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