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

Step 1: Given data:
Number of car $A$ owners $=n\left(A\right)=400$
Number of car $B$ owners $=n\left(B\right)=200$
Number of car $A$ and car $B$ owners $=n(A\cap B)=50$

Step 2: Solve for $n(A\cup B)$
$n(A\cup B)=n\left(A\right)+n\left(B\right)-n(A\cap B)$
$=400+200-50$
$\therefore n(A\cup B)=550$
Number of people who owned either car $A$ or car $B=550$
And Total number of car owners $=500$ (given)
Number of people who own car $A$ or car $B$ should be less than or equal to total number of car owners investigated.
But $550>500$, which is contradiction.
So, given data is incorrect.