Question

There are $19$ hockey players in a club. On a particular day $14$ were wearing the prescribed hockey shirts while $11$ were wearing the prescribed hockey paints. None of them was without a hockey pant or a hockey shirt. How many of them were in complete hockey uniform ?

• A. $8$
• B. $6$
• C. $9$
• D. $7$

Answer 1

The correct option is B $6$

Let $P$ and $S$ represents the sets of hockey player wearing the prescribed hockey pants and shirts respectively.
Then $n\left(P\right)=11$, $n\left(S\right)=14$, $n$$(P\cup S)$ $=19$
$\Rightarrow$ $(P\cap S)$ $=$ no of people wearing both pantand shirt
$=n\left(P\right)+n\left(S\right)-n$$(P\cup S)$
$=11+14-19=6$