Am I right or is the book wrong

I'm studying for the math placement test for my future high school. The book says find the inverse of "if not p, then q" I think it is "if p, then not q" but the book says it's "if p, then q."

I'm confused I thought I knew what inverses are. Dx Please help and thank you

You are right and the book is wrong :)

Using the standard definition of inverse, the inverse of "if not p, then q" is "if p, then not q", as you stated. Sometimes books make typos, frustrating as it is.

The inverse of the statement "If p then q" is "If not p then not q".

So the inverse of "if not p then q" is "if not (not p) then not q", or "If p then not q".

You are correct, and the book is wrong.

Therefore the logical answer to your question is "Yes" (both apply).

The question is the inverse of:
(not p) implies q (this is a contradiction)

You have
p implies (not q) (this is still a contradiction)

This is the same. Think of it as:
-p=q then you just wrote p=-q which is still the same.

You need the inverse so of the contradiction (e.g. a truth)
-p=q become p=q
(not p) implies q becomes:
p implies q because this is the truth (e.g. inverse of a contradiction).

The inverse of "if not p, then q" is "if p, then not q".