Suppose I am trying to prove a statement in the form A if and only if B. I know I need to prove that
- If A, then B
- If B, then A
I know that 1 is equivalent to proving "If not B, then not A".
My question is: When proving A if and only if B, is it permissible to prove "if not B, then not A" and then "if B, then A."
I have seen many people prove A iff B by showing "If not A, then not B" and then "If not B, then not A," but never the way I described, which is why I am asking if it is okay.
$\endgroup$ 21 Answer
$\begingroup$Yes that is perfectly fine. A implies B is logically equivalent to "not B, then not A".
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