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If $S$ and $T$ are two sets such that $S$ has 21 elements, $T$ has 32 elements, and $S \cap T$ has 11 elements, how many elements does $S \cup T$ have?
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Here, $n(S)=21$ and $n(T)=32$
and $n(S \cap T)=11$
Now, $n(S \cup T)=n(S)+n(T)-\mathrm{n}(S \cap T)$
$=21+32-11=53-11=42$.
and $n(S \cap T)=11$
Now, $n(S \cup T)=n(S)+n(T)-\mathrm{n}(S \cap T)$
$=21+32-11=53-11=42$.
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