Converse implication ($B\to A$)

The converse implication of $A\to B$ is $B\to A$. It exchanges hypothesis and conclusion without logical negation. It need not follow from the original logical implication: $n=2$ is an even number but is not divisible by four. Thus “being an even number implies divisibility by four” is false, although the original implication holds for all natural numbers. Proving both directions establishes an “if and only if” statement; proving a contrapositive establishes the original implication classically, without establishing its converse implication.