Prove the validity of this: (~h V j) V k - premise 1, k -> ~i - premise 2, therefore (h & i) -> j?

Question

Its a philosphy question, using propositional logic.

Answer 1

assuming you have conditional argument as an inference rule:

1. (-h v j) v k .......... prem
2. k → -i .................prem
3. h & i .................asmp for CP
4. i .......................3 simp (and maybe commutative, if teacher strict)
5. -k .....................2, 4, modus tolens
6. -h v j ................1, 5, disjunctive syllogism (or whatever name your book uses)
7. h ...................... 3 simplification
8. j .......................6, 8, disj syll
9. (h&i) → j ........... 3, 8, conditional proof.

it's much longer without conditional proof.