Question

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?

Answer 1

Here

$n\left(S\right)=21,n\left(T\right)=32$

and $n(s\cap T)=11$

We know that

$n(S\cup T)=n\left(S\right)+n\left(T\right)-n(S\cap T)$

$\therefore$ $n(S\cup T)=21+32-11=42.$