logic/proof

[richardt]

Greetings:

In proving P --> Q V R, is it sufficient so show (P and Q') implies R?

It seems right to me as, Q can either hold or not. If it does, then the proof is complete. Else, R holds. Either way, If P, then Q or R is demonstrated.

Thanks,
Rich

 

[pka]

In proving P --> Q V R, is it sufficient so show (P and Q') implies R?

\(\displaystyle \\p \to \left( {q \vee r} \right)\\\neg p \vee \left( {q \vee r} \right)\\\left( {\neg p \vee q} \right) \vee r\\\neg \left( {p \wedge \neg q} \right) \vee r\\?\)