Question: Use logical equivalnces to show that the propositions !p -> (q->r) and q -> (p v r) are logically equivalent.

Question

I AM SO DAMN CONFUSED!

I tried to solve !p -> (q -> r) first

and I only got to !p -> (!q v r)

I cant see any other rule that would apply after i get that far! Someone with some knowledge please help!

Answer 1

You'll need the logical equivalence:
p → q ≡ !p ∨ q

so
!p → (q→r)
≡ p ∨ (!q ∨ r)

From here, use the commutative properties to rearrange the expression and apply the equivalence (of →) again to get the desired result.