If P--> q false, can truth value of (~p)V(p<-->q) be found?

[cshw20]

Q: If P --> q is false, can you determine the truth value of (~p) V (p<-->q)?

My answer:

Yes. If p-->q is false then p is T and q is F.
p<-->q = ((p-->q) ^ (q-->p)) = contradiction = F
If p is T then ~p is F.
F V F = F

Please tell me if I am mistaken.

Thank you.

 

[stapel]

Q: If P --> q is false, can you determine the truth value of (~p) V (p<-->q)?

I don't see how, unless you have information (omitted from your post) relating P to either or both of p and q...? :?:

All you can tell with a truth-table for P, q, and P-then-q is the truth values of P and q. But this won't help you evaluate expressions containing the third variable, p. :shock:

Eliz.

 

[cshw20]

Re: Logic question

My apologies, the initial "P" in the question should have been a lower case p.

 

[stapel]

In that case, use the truth-value of the initial statement to find the truth-values of p and q. Plug these into a truth-table, and find the truth-value of the second statement. :wink:

Eliz.