Symbolic Argument, Find valid conclusion and justify.
It's me again, lol.
Find a valid conclusion to the argument given bwlow in symbolic form. Justify your answer.
~p (p^ ~q) ------ premise 1
q --> r --------- premise 2
~ r -------------- premise 3
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therefore, ?
Here is what I did last night,
1. ~r PIII
2. ~r-->~q PII, contrapositive
3. ~q 1,2,detachment
4. ~p v q PI, DeMorgan's Laws
5. ~p 3,4,disjunctive syllogism
therefore, ~p. not sure if this is right or my work is right, thanks in advance.