Which of the following pairs of sets are equal? Justify your answer.
$X$,the set of letters in "$ALLOY$" and $B$,the set of letters in "$LOYAL$".
$X$,the set of letters in "$ALLOY$" and $B$,the set of letters in "$LOYAL$".
(A) We have,$X = \{A, L, L, O, Y\} = \{A, L, O, Y\}$ and $B = \{L, O, Y, A, L\} = \{L, O, Y, A\}$.
Since the repetition of elements in a set does not change the set,we have $X = \{A, L, O, Y\}$ and $B = \{A, L, O, Y\}$.
Since all elements of $X$ are in $B$ and all elements of $B$ are in $X$,the sets are equal.
Thus,$X = B$.
Since the repetition of elements in a set does not change the set,we have $X = \{A, L, O, Y\}$ and $B = \{A, L, O, Y\}$.
Since all elements of $X$ are in $B$ and all elements of $B$ are in $X$,the sets are equal.
Thus,$X = B$.
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