Question

Out of $500$ car owners investigated, $400$ owned car $A$ and $200$ owned car $B,50$ owned both $A$ and $B$ cars. Is this data correct?

Answer 1

Let $U=$ set of car owners investigated
$M=$ set of persons who owned car $A$
$S=$ set of persons who owned car $B$
Then $n\left(u\right)=500,n\left(M\right)=400,n\left(S\right)=200$ and $n(S\cap M)=50$
$\therefore n(S\cup M)=n\left(S\right)+n\left(M\right)-n(S\cap M)$
$=200+400-50=550$
But $S\cup M\subset \Rightarrow n(S\cup M)\le n\left(U\right)$
This is contradiction. So, the given data is incorrect