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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:
and here is the writer's answer:
and here is my answer:
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.
