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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