Conditional statement truth table reasoning.

Question

Let P be the Hypothesis and Q be the conclusion.

I believe I understand the logic of If P then Q in the two case where,

A. P is True and Q is false. B. P is True and Q is true.

the two cases where I'm having a trickier time fully understanding what is going on are,

C. P is False and Q is True. D. P is False and Q is False.

A line of reasoning that I've heard expressed are that, if P is False it cannot be said whether or not Q is True.

If this is the case, why is it that C. and D. return values of True rather than values of Undetermined?

How can you know the truth of the statement if when P is false, you cannot make a conclusion?

Thank you for your valuable time!

There are a few answers on this site, such as this one. – twosigma May 18 '20 at 22:31 — twosigma, May 18 '20 at 22:31

score 0 · Answer 1 · answered May 18 '20 at 22:31

0

HINT: consider $p=q$, both false, for example "If $2$ is odd, then $2$ is odd". Can you say that the implication is false?

answered May 18 '20 at 22:31

Maryam

1

Please don't answer a question with a question. While you may think your question has an obvious answer, the OP is asking for an explanation. And your example only covers one of the two cases the OP asked about. – amWhy May 18 '20 at 22:33

1 Answers1