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
-----------------------------------------
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.

Quote:

---

Originally Posted by stueycal

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

---

Look at premise 1.
It does not seem to be correct.
Please correct it.

~(p^ ~q) ------ premise 1
q --> r --------- premise 2
~ r -------------- premise 3

whoops.

Quote:

---

Originally Posted by stueycal

~(p^ ~q) ------ premise 1
q --> r --------- premise 2
~ r -------------- premise 3

---

Premises 2&3 give $\displaystyle \neg q$ by Modus Tollens.
From premise 1 and DeMorgan's Theorem we get $\displaystyle \neg p \vee q $.
Then by Disjunctive Syllogism we get $\displaystyle \neg p$.