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?
Thank you for your help.
Hi Jocelyn. The answer is Yes to your four questions.
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,
if Q is true, then [(P v not-P) implies Q] is true.
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.
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"?
Thank you again, Avi.
Most kind of you.