Question

i'm confused on this, help?
is p is true and q is false.

Is (p -> q) true or false?

Answer 1

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I am studying entailment in classical first-order logic.

The Truth Table we have been presented with for the statement (p⇒q)(p⇒q) (a.k.a. 'pp implies qq') is:
pTTFFqTFTFp⇒qTFTT
pqp⇒qTTTTFFFTTFFT
I 'get' lines 1, 2, and 3, but I do not understand line 4.

Why is the statement (p⇒q)(p⇒q) True if both p and q are False?

We have also been told that (p⇒q)(p⇒q) is logically equivalent to ( p||q)( p||q) (that is ¬p∨q¬p∨q).

Stemming from my lack of understanding of line 4 of the Truth Table, I do not understand why this equivalence is accurate. i fond this

Answer 2

"if P, then Q" is false: namely, P is true and Q is false.

Answer 3

yup

Answer 4

lol alibaby threw me off a little but i seem to understand what you mean, thank you both!

Answer 5

but what about if it looks like this -q then -p?