Show that the set of letters needed to spell

Question:

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

Solution:

Letters required to spell CATARACT are {C, A, T, R}. Let this set be denoted as E.

{C, A, T, R}

Letters required to spell TRACT are {T, R, A, C}. Let this set be denoted as F.

F = {T, R, A, C}

The two sets E & F are equal because every element of E is a member of F & every element of F is a member of E.

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