If my plumbing plans do not meet the construction code, then I cannot build my house.
If I hire a licensed contractor, then my plumbing plans will not meet the construction code.
I hire a licensed contractor.
Therefore I can build my house.
Prove by rule of inference is the argument valid or invalid :
below is my attempt
Premise 1: $\neg P \rightarrow \neg Q$
Premise 2: $R \rightarrow \neg P$
Premise 3: $R$
Conclusion: $Q$
and to further prove the validity i used this method :
Premise 4 : $P \rightarrow Q$ (Inverse of premise 1)
Premise 5 : $\neg P$ (Modus ponens of premise 2 + 3)
Premise 6 : $\ P$ (negation of premise 5)
$\ Q$ (Modus ponens of premise 4 and premise 6)
Best Answer
Welcome! it's a good attempt, you almost have it.
Consider,
Premise 1: $\neg P \rightarrow \neg Q$
Premise 2: $R \rightarrow \neg P$
Premise 3: $R$
By premise (2) and (3) + Modus Ponens we have: $ \neg P$
So,
premise 4: $ \neg P$
by premise (1) and (4) + Modus Ponens
Conclusion: $\neg Q$
What can you say, about the truth of Q, given the above argument?