I think about it like this: denying the existence of a square does not deny the existence of rectangles.

This all made sense but after all the drilling on conditional logic my brain was in formal argument mode and kept looking to use lawgic on problems where it wasn't applicable.

Is taking the contrapositive a final necessary step to getting the correct answer? or can we translate back into English after negating one of the ideas and making it the sufficient?

my predicate logic professor would lose his mind if i told him i was conflating categorical syllogism and modus ponens