Show that the set of letters needed to spell "$CATARACT$" and the set of letters needed to spell "$TRACT$" are equal.
(N/A) 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 $X = Y$.
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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