Show that the set of letters needed to spell $"\mathrm{CATARACT}"$ and the set of letters needed to spell $"\mathrm{TRACT}"$ are equal.
Show that the set of letters needed to spell $"\mathrm{CATARACT}"$ and the set of letters needed to spell $"\mathrm{TRACT}"$ are equal.
Let $X$ be the set of letters in $"CATARACT".$ Then
$X=\{ C , A , T , R \}$
Let $Y$ be the set of letters in $"TRACT".$ Then
$Y=\{T, R, A, C, T\}=\{T, R, A, C\}$
Since every element in $X$ is in $Y$ and every element in $Y$ is in $X$. It follows that $X = Y$.
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