Show that set of letters needed to spell "mathrm{CATARACT}" and set of letters needed to s

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1.Set Theory

easy

Show that the set of letters needed to spell $"\mathrm{CATARACT}"$ and the set of letters needed to spell $"\mathrm{TRACT}"$ are equal.

Option A

Option B

Option C

Option D

Solution

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 $X = Y$.

Standard 11

Mathematics

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