Does a statement need to be a biconditional statement to prove by the contrapositive I am trying to write a proof and was wondering if a then b, the converse if b then a might not be true. This leads me to wonder if the statement needs to be an if and only if statement if it can be proven by the contrapositive if not b then not a.
That is do I need a statement like this a if and only if b to prove that if not b then then not a, or is if a then b sufficient to do that.

By definition, "$a \implies b$" means "not ($a$ and not $b$)". So then "(not $b$)$\implies$(not $a$)" means "not ((not $b$) and not (not $a$))". This simplifies to "not ($a$ and not $b$)", which is the same thing as "$a \implies b$". So yeah, you only need the one direction of implication.
You should probably think about this definition of $a \implies b$ if you've never seen it. Like, draw a truth table or something.
