### The Logic Forum Discussion Area Logic
Author
Comment
A tautology used in implication

I understand that a contradiction implies anything, but what about a tautology?

(P V not-P) is a tautolgoy, right?

so if we say (P v not-P) implies Q, isn't this the same as just saying Q?

And if Q is true then [(P v not-P) implies Q] is true. and if Q is false, then [(P v not-P) implies Q] is false, right?

Re: A tautology used in implication

P or not-P = (if not P, then not-P) and (if not not-P, then P) = tautology.

Given: (if P then P) then Q,
since: (if P then P) is true for all P,
therefore: Q.

Whence,
if Q is true, then [(P v not-P) implies Q] is true.
and
if Q is false, then [(P v not-P) implies Q] is false.

Notice that I use if-then statements rather than disjunctions (v), because the former are closer to natural thinking.

Just lay it all out. point by point.

Re: A tautology used in implication

Thank you, Avi.

If I do the truth table for some logic statement (such as [(P v not-P) implies Q] and I get all T's for the (P v not-P) part, that means the (p v not-p) part is a tautology, right?

But the whole thing [(P v not-P) implies Q] is not a tautology, right?

Is there a name for such a construction, besides "pointless"?

Re: A tautology used in implication

the (p v not-p) part is a tautology

the whole thing [(P v not-P) implies Q] is identical with Q - so it is a tautology of Q.

all this is indeed pointless,

but I guess it is intended as exercise. enjoy!

Re: A tautology used in implication

Thank you again, Avi.

Most kind of you.