I've tried numerous ways at solving this problem but am stuck. I believe I need to use logical equivalences involving conditionals, De Morgan's law, associative law and distribution (I've used them below however most likely incorrectly). Here is the question and a way I've tried solving it. I need to do this without the use of truth tables by the way. To be clear I'm trying to find out if the beginning statement is a tautology, contradiction, or contingency. Thanks all!
((p v q) ∧ (￢q v ￢r)) → (r → p) ≡
￢((p v q) ∧ (￢q v ￢r)) ∨ (r → p) ≡
￢((p v q) ∧ (￢q v ￢r)) ∨ (￢r v p) ≡
￢((p v q) ∧ (￢q v ￢r)) ∨ ￢(r ∧ ￢p) ≡
￢(((p v q) ∧ (￢q v ￢r)) ∨ (r ∧ ￢p)) ≡
￢((p v q) ∧ ((￢q v ￢r)) ∨ (r ∧ ￢p))) ≡
And I seem to get stuck in here when trying to use the distributive property to perhaps evaluate one of these statements to true/false.