Question

How many play hockey only?

Answer 1

Let A and B be the sets of those playing hockey and cricket, respectively.
Then $n\left(A\right)=28$, $n\left(B\right)=33$ and $n(A\cup B)=60-14=46$.
Number of pupils who play hockey only $=n\left(A\right)=n(A\cup B)-n\left(B\right)=46-33=13$.
Note: The formulae used above can be extended for more than two sets also.
For any three sets A, B, and C,
$n(A\cup B\cup C)=n\left(A\right)+n\left(B\right)+n\left(C\right)-n(A\cap C)-n(B\cap C)-n(A\cap C)+n(A\cap B\cap C)$