I’m reading Introduction to Logic by Harry J. Gensler. I reached to Part Two, Chapter 7, Propositional Proofs (Easier proofs, s- and l-rules, RAA, how to derive, refutation…etc.)

What is the difference between what I did and what the author did?

here is the question: enter image description here

and here is the writer's answer: enter image description here

and here is my answer:

enter image description here


1 Answer 1


Your step 7 is wrong.

See Contraposition: (∼W ⊃ ∼G) is equivalent to (G ⊃ W).

From (∼W ⊃ ∼G) and G we cannot validly infer ∼W. Consider the case when G and W are both TRUE: in this case the premises (∼W ⊃ ∼G) and G are TRUE but the conclusion ∼W is FALSE.

  • Thanks for your help. It seems that the book did not refer to this point that you mentioned, and that is why I made a mistake in my answer. I think I misunderstood the words of the writer (page 148): here image.ibb.co/jgYEfw/Capture.png Nov 11, 2017 at 15:31
  • 1
    @MohammadAltamimi - exactly: see bottom left: from (∼A ⊃ ∼B) and B, derive A. Nov 11, 2017 at 16:23

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