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[Apprentice123]

How to check if the argument is valid

(1) p -> ~q
(2) p ^ r
-----------
|- q


I did:

(1) p -> ~q
(2) p ^ r
(3) ~p v ~q SWITCHEROO (1)
(4) ~(p^q) DeMorgan (3)
(5) (p^r) ^ ~(p^q) CONJUNCTION (2,4)
What rule can I apply now?

[WingedPanther]

Try doing the truth table for ((p -> ~q) ^ (p ^ r)) -> q and seeing if it's a tautology. My expectation is it is not. For example, p = T, q=F makes first true, r=T makes second true as well, but conclusion is false.