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In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?
Solution:
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Verified Answer
Let $C=$ the set of people who like cricket and $T=$ the set of people who like tennis.
Then, $n(C \cup T)=65, n(C)=40$
$n(C \cap T)=10$
We know that
$\begin{aligned}
& n(C \cup T)=n(C)+n(T)-n(C \cap T) \\
\Rightarrow & 65=40+n(T)-10 \\
\Rightarrow & n(T)=65-30=35
\end{aligned}$
Number of people who like only tennis
$\begin{aligned}
&=n(T)-n(C \cap T) \\
&=35-10=25
\end{aligned}$
Hence, number of people who like tennis is 35 and number of people who like tennis only is 25 .
Then, $n(C \cup T)=65, n(C)=40$
$n(C \cap T)=10$
We know that
$\begin{aligned}
& n(C \cup T)=n(C)+n(T)-n(C \cap T) \\
\Rightarrow & 65=40+n(T)-10 \\
\Rightarrow & n(T)=65-30=35
\end{aligned}$
Number of people who like only tennis
$\begin{aligned}
&=n(T)-n(C \cap T) \\
&=35-10=25
\end{aligned}$
Hence, number of people who like tennis is 35 and number of people who like tennis only is 25 .
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