Seth M. answered • 11/06/16

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There are two ways of answering this question. The most comprehensive would be to use a truth table (which I cannot do in this system). The other is to use the rules of inference to show how you can get from one form to the other, as follows:

(p -> (q -> r))

(p -> (~q v r)) Material Implication

(~p v (~q v r)) Material Implication

(~p v (r v ~q)) Commutativity

((~p v r) v ~q) Associativity

(~(~p v r) -> ~q) Material Implication

((p ^ ~r) -> ~q) DeMorgan's Rule

And there you have it. There may be a more direct way to get there, but that is what came to me this morning. :)