Question

If $S$ and $T$ are two sets such that $S$ has $21$ elelments, $T$ has $32$ elements and $S\cap T$ had $11$ elements, how many elements does $S\cup T$ have?

Answer 1

Given :
$n\left(S\right)=21,n\left(T\right)=32,n(S\cap T)=11$
Solve for $n(S\cup T)$
$n(S\cup T)=n\left(S\right)+n\left(T\right)-n(S\cap T)$
$\Rightarrow n(S\cup T)=21+32-11$
$\Rightarrow n(S\cup T)=53-11$
$\Rightarrow n(S\cup T)=42$
Thus, the set $(S\cup T)$ has $42$ elements.

Final answer:
$n(S\cup T)=42$.