[Math] Checking Validity of Arguments using Rules of Inference

Question

Im trying to understand how a theorem or statement is proved using Rules of Inference.I have this example

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I really don't understand how they say.Now p->q may be true with p being false.Then conclusion of p is false.Hence the argument is not valid

What i know is the proposition p->q is only false when p is true and q is false.From that how can they say that if p>q is true when p is false then conclusion is false.Can someone explain the logic in layman's terms please.

• Im referring Discrete Mathematical Structures by Kolman,Busby and Ross

EDIT:

Answer 1

But he assume that $p \to q$ is true !

This is possible also with $p$ false and $q$ true.

In this case, we have both : $p \to q$ true and $q$ true ("assume that $p \to q$ and $q$ are both true"), and the conclusion $p$ will be false.

Thus :

the argument is invalid.