Question

If a b and c are three sets and U is the universal set such that n(U)=700 ,n(a)=200, n(b)=300 and find n(a intersection b) =100. Find n(a compliment intersection b compliment).

Answer 1

$\textbf{Given:}$

$n(U)=700,\;n(A)=200,\;n(B)=300,\;n(A{\cap}B)=100$

$\text{Using}$

$\boxed{\bf\,n(A{\cup}B)=n(A)+n(B)-n(A{\cap}B)}$

$n(A{\cup}B)=200+300-100$

$n(A{\cup}B)=400$

$\text{Now}$

$n(A'{\cap}B')$

$=n((A{\cup}B)')$

$=n(U)-n(A{\cup}B)$

$=700-400$

$=300$

$\implies\boxed{\bf\,n(A'{\cap}B')=300}$