Formal logic statements symbolic representation.

Question

If the horse is fresh, then the knight will win. $H -> K$ A fresh horse is a necessary condition for the knight to win. $K -> H$

I think the first sentence should have same notation. I don't understand why are different.

Answer 1

$p \implies q$ is not the same as $q \implies p$. $q \implies p$ is the converse of $p\implies q$. In other words they are not logically equivalent. Make a truth table and you’ll see why.