Question

If $X$ and $Y$ are two sets such that $X\cup Y$ has $50$ elements,$H$ has $28$ elements and $Y$ has $32$ elements,how many elements does $X\cap Y$ have?

Answer 1

Given $n(X\subset Y)=50;n\left(X\right)=28;n\left(Y\right)=32$
But $n(X\cup Y)=n\left(X\right)+n\left(y\right)-n(X\cap Y)$
$\therefore n(X\cap Y)=28+32-50=10$