Contrapositive on "If and only if" with one negative

Let's say you have the statement "A if and only if not B." The diagram would be A <-> not B. Would the contrapositive be not A <-> B? If you could explain the logic behind this, that would be greatly appreciated.

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Emil-Kunkin April 15, 2022

Hi Bradley,

I would start this by breaking this out into the if and then only if.

the "if" is

If Not B - A
the contrapositive of this is
If Not A - B

The only if is "A only if Not B"

If A - Not B
If B -Not A