What is the inverse of the conditional statement 'If p, then q'?

Prepare for the Geometry CBE Exam with targeted resources. Access interactive quizzes and detailed explanations to master geometric concepts effectively and excel in your test!

The main idea is that the inverse of a conditional keeps the same structure but negates both parts. For “If p, then q,” you switch p to not p and q to not q while keeping the order, giving “If not p, then not q.”

That’s why this form is the correct one. It’s the statement you get when you ask what happens if p doesn’t happen: then q also doesn’t happen. It’s distinct from the converse (which would swap p and q: “If q, then p”) and from the contrapositive (which negates both parts but reverses them: “If not q, then not p,” which is actually equivalent to the original). The original remains “If p, then q.”

A helpful mental image: p might be “you study,” q might be “you pass.” The original says studying implies passing. The inverse says if you don’t study, you don’t pass. The truth of the original doesn’t guarantee the inverse, but that’s a separate matter from how the inverse is formed.