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If $X$ and $Y$ are two sets such that $X$ has 40 elements, $X \cup Y$ has 60 elements and $X \cap Y$ has 10 elements, how many elements does $Y$ have?
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$\begin{aligned} \text { Here, } & n(X)=40 \\ & n(X \cup Y)=60 \\ & n(X \cap Y)=10 \\ \text { Now, } & n(X \cup Y)=n(X)+n(Y)-n(X \cap Y) \\ \Rightarrow & 60=40+n(Y)-10 \\ \Rightarrow & n(Y)=60-40+10=20+10=30 \end{aligned}$
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