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Answer to Question #16770 in Discrete Mathematics for nelly

Question #16770
let A be{1,2,3,4,11} let B be{2,4,5,6,9} and C be {1,3,7,8,10}
find 1.(A-B)-C
2.(A-C)-(B-C)
3.is (A-B)-C=(A-C)-(B-C)
Expert's answer
1. (A-B)-C
we must find at first (A-B) its the set of elements that belongs
to A but not to B
(A-B)={1,3,11}
then (A-B)-C that elements that in the
(A-B) but not in C
(A-B)={1,3,11}, C={1,3,7,8,10} and we see that
(A-B)-C={11}

2. (A-C)-(B-C) we must find (A-C) and (B-C) in the such way
as in the 1.
D=(A-C)={2,4,11}
E=(B-C)={2,4,5,6,9}
and now we find
(A-C)-(B-C)=D-E
and D-E={11}

3. we see that (A-B)-C=(A-C)-(B-C)

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