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I'm trying to prove this argument is valid:

Hypotheses:

  1. $(p$ or $q)$ implies $r$
  2. not $r$
  3. $q$

Conclusion: not $p$

I used modus tollens on steps 1 and 2 to get not $(p$ or $q).$

Then I distributed the not sign using De Morgans law to get not $p$ or not $q.$

Then I grouped the not $p$ or not $q$ and the 3rd hypothesis to get not $p$ using disjunctive syllogism.

Is this correct? I'm not if the disjunctive syllogism step is correct because of the signs.

ryang
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Alex S.
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  • Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Apr 16 '22 at 06:03

1 Answers1

1

Hint:

not $(p$ or $q).$ Then I distributed the not sign using De Morgans law to get not $p$ or not $q.$

This step is incorrect.

After making this correction, you will find that the premises are inconsistent.

ryang
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