SOLUTION: Choose one of the proofs below and use one of the indirect proof techniques (reductio ad absurdum or conditional proof) presented in Chapter 8 to demonstrate the validity of the ar

Question 1125684: Choose one of the proofs below and use one of the indirect proof techniques (reductio ad absurdum or conditional proof) presented in Chapter 8 to demonstrate the validity of the argument. The proofs below may use any of the rules of inference or replacement rules given in Chapter 8.
(G � P) → K, E → Z, ~P → ~ Z, G → (E v L), therefore, (G � ~L) → K
(S v T) ↔ ~E, S → (F � ~G), A → W, T → ~W, therefore, (~E � A) → ~G
(S v T) v (U v W), therefore, (U v T) v (S v W)
~Q → (L → F), Q → ~A, F → B, L, therefore, ~A v B
~S → (F → L), F → (L → P), therefore, ~S → (F → P)

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

I'm going to pick on the first line
(G � P) → K, E → Z, ~P → ~ Z, G → (E v L), therefore, (G � ~L) → K
to prove that out.

I'll do so in two ways. The first of which is through a conditional proof

Start with the antecedent of the conclusion, which is (G & ~L) and show how it leads to K

note: I used an ampersand in place of a dot

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Then I'll show how to do a proof by contradiction (aka reductio ad absurdum), which is an indirect proof.

The idea is to assume the complete opposite the conclusion, and then show how a contradiction arises.

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