https://maximummathematics.com/books/foundational-mathematics/proof/proof-technique-equivalence/index.htmlAll of the proof techniques we’ve discussed so far only seem to go one way. When we provide a proof for $a \Longrightarrow b$, what we’re really saying is that if $a$ is true, then $b$ is true too — but since an implication isn’t generally logically equivalent to its converse, we can’t go the other way: knowing $b$ is true doesn’t necessarily tell us $a$ is also true. However, just because that’s true in general doesn’t mean there are never instances where an implication is logically equivalent to its converse. Consider the statement $n \text{ is even} \Longrightarrow n + 1 \text{ is odd}$. Clearly, its converse is also a logical implication: $n + 1 \text{ is odd} \Longrightarrow n \text{ is even}$. So, whenever “$n$ is even” is true, “$n + 1$ is odd” is also true — and vice versa. These propositions are either simultaneously true, or simultaneously false. Hence, we can write $n \text{ is even} \Longleftrightarrow n + 1 \text{ is odd}$.Hugoen-US