What is the reason that a hypothesis is false so that the conclusion, the p-q, becomes true?

Answer 1

If p then q

p --> q

if the hypothesis is false, NOTHING can be said about the conclusion;

So they assign the value TRUE to the ENTIRE STATEMENT.

Therefore the truth table looks like this:

p q p-->q

==============================

T T T

T F F

F T T

F F T

Think of it like this.....

"If you are bad, THEN you get punished..."

p = you are bad

q = you get punished

If both statements are true, then you are bad, so you got punished.

Therefore, the entire statement is true, because the consequence follows the hypothesis as expected.

second case:

If you are bad, but you DID NOT get punished.

Then you got away with being bad and the consequence did NOT follow as expected.

So the entire statement is false ( it is a LIE)

third case, this is the one you are asking about:

If you are GOOD, then you get punished.

Not fair to you, but you got punished for doing something else.

They label the statement, in and of itself, as true

fourth case:

if you are GOOD then you DO NOT get punished.

The entire statement is the INVERSE of the original and is true.

Everybody wins.