Out of $500$ car owners investigated, $400$ owned car $\mathrm{A}$ and $200$ owned car $\mathrm{B} , 50$ owned both $\mathrm{A}$ and $\mathrm{B}$ cars. Is this data correct?
Out of $500$ car owners investigated, $400$ owned car $\mathrm{A}$ and $200$ owned car $\mathrm{B} , 50$ owned both $\mathrm{A}$ and $\mathrm{B}$ cars. Is this data correct?
Let $U$ be the set of car owners investigated, $M$ be the set of persons who owned car $A$ and $S$ be the set of persons who owned car $B.$
Given that $\quad n( U )=500, n( M )=400, n( S )=200$ and $n( S \cap M )=50$
Then $\quad n( S \cup M )=n( S )+n( M )-n( S \cap M )=200+400-50=550$
But $S \cup M \subset U$ implies $n( S \cup M ) \leq n( U )$
This is a contradiction. So, the given data is incorrect.
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