How do I solve this equation with logical equivalence laws?

Question

The problem is :

Show that ¬ p → (q → r) and q → (p v r) are logically equivalent.

I'm having trouble proving this with the use of Logical Identities. Any help is much appreciated.

Answer 1

See this can be proved like this.

 ~p --> (q --> r)   
 ~~p v (q --> r)    -- (p -->q = ~p v q)   --Implication law
 p v (~q v r)       -- (~ (~p) = p )       -- Double negation law
 ~q v (p v r)       -- (P ∨ (Q ∨ R) ≡ (P ∨ Q) ∨ R)  -- associativity Law
 q --> (p v r)                             -- Implication law