g --> h
~h v k
g
k --> w
Prove: W
To prove that W is true, we can use deductive reasoning and apply the rules of inference to the given premises:
1. g -> h (Premise)
2. ~h v k (Premise)
3. g (Premise)
4. ~h (Modus Ponens using 1 and 3)
5. k (Disjunction Elimination using 2 and 4)
6. k -> w (Premise)
7. w (Modus Ponens using 5 and 6)
Therefore, we have successfully derived the conclusion that W is true.