Out of 500 car owners investigated, 400 owned car mathrm{A} and 200 owned car mathrm{B} , 50 owned b

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1.Set Theory

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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?

Option A

Option B

Option C

Option D

Solution

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.

Standard 11

Mathematics

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