A∖B=B∖A<=>A=B can we actually prove it without using contradiction?
Jaylyn Gibson
Answered question
2022-08-06
can we actually prove it without using contradiction?
Answer & Explanation
Howard Robertson
Beginner2022-08-07Added 6 answers
if , then . If , then without loss of generality there is some that is not in . But then and , so . If you began by assuming that , this is a proof by contradiction, but that assumption is unnecessary: without it you have a direct proof of the contrapositive of the original implication.
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