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If $X$ and $Y$ are two sets such that $n(X)=17, n(Y)=23$ and $\mathrm{n}(X \cup Y)=38$, find $n(X \cap Y)$
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Verified Answer
We know that
$\begin{aligned}
&n(X \cup Y)=n(X)+n(Y)-n(X \cap Y) \\
&\Rightarrow 38=17+23-n(X \cap Y) . \Rightarrow 38=17+23-\mathrm{n}(X \cap Y) \\
&\Rightarrow n(X \cap Y)=40-38=2
\end{aligned}$
$\begin{aligned}
&n(X \cup Y)=n(X)+n(Y)-n(X \cap Y) \\
&\Rightarrow 38=17+23-n(X \cap Y) . \Rightarrow 38=17+23-\mathrm{n}(X \cap Y) \\
&\Rightarrow n(X \cap Y)=40-38=2
\end{aligned}$
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