Show that the set of letters needed to spell “CATARACT” and the set of letters needed to spell “TRACT” are equal.

Solution: Let Set $P$ is the set of letters needed to spell $\text{CATARACT}$. Then,
$P=\left\{C,A,T,R\right\}$
Let Set $Q$ is the set of letters needed to spell $\text{TRACT}$. Then,
$Q=\left\{T,R,A,C\right\}$
As both sets $P$ and $Q$ are having same elements, it means, $P=Q$.