This is an example exam question that I'm wondering if I did right? We weren't given an answer key, so I'm checking to make sure I'm comprehending the material and if my answer is correct?

Premises: P $\Rightarrow$ Q, (P $\Rightarrow$ Q) $\Rightarrow$ (T $\Rightarrow$ S), $\lnot$Q, P $\lor$ T

Conclusion: S

My answer:

  1. P $\Rightarrow$ Q: Given

  2. (P $\Rightarrow$ Q) $\Rightarrow$ (T $\Rightarrow$ S): Given

  3. $\lnot$Q: Given

  4. P $\lor$ T: Given

  5. T $\Rightarrow$ S: Modus Ponens 1 and 2

  6. $\lnot$P: Modus Tollens 1 and 3

  7. T: Disjunctive Syllogism 4 and 6

  8. S: Modus Ponens 5 and 7

  • 3
    $\begingroup$ It's correct.${}$ $\endgroup$
    – Git Gud
    Feb 16, 2015 at 23:02
  • 1
    $\begingroup$ Yep, looks good. $\endgroup$
    – Joffan
    Feb 16, 2015 at 23:13

2 Answers 2


This proof is correct according to this proof checker:

enter image description here

Modus ponens is conditional elimination on lines 5 and 8.


The proof seems fine. This is a community wiki post so that the question is not marked as unanswered.


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