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Hey guys, I'm asked to show the following arguments are valid:

1) $p\rightarrow q$
2) $(q\lor r)\land (\lnot (q\land r))$

Therefore:
3) $\lnot q\rightarrow (\lnot p\land r)$

I know you need to use the rules of inference like modus ponens/converse fallacy but I'm confused because it doesn't look like any of the forms I've learned about?

Thanks

[Edit: corrected parentheses in line 3]

  • 1
    If $p$ implies $q$ and exactly one of $q$ and $r$ is true, then the failure of $q$ implies that $p$ is false and $r$ is true. It's obvious, isn't it?2011-04-29
  • 0
    Hmm yes so the second statement says either q or r but not both. Now that you mention it like that I'm thinking about the second statement differently and it's much clearer, thanks!2011-04-29

3 Answers 3