PHI103 Southern New Hampshire Indirect Proofs in Natural Deduction Paper

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.
1.(G • P) †’ K, E †’ Z, ~P †’ ~ Z, G †’ (E v L), therefore, (G • ~L) †’ K
2.(S v T) †” ~E, S †’ (F • ~G), A †’ W, T †’ ~W, therefore, (~E • A) †’ ~G
3.(S v T) v (U v W), therefore, (U v T) v (S v W)
4.~Q †’ (L †’ F), Q †’ ~A, F †’ B, L, therefore, ~A v B
5.~S †’ (F †’ L), F †’ (L †’ P), therefore, ~S †’ (F †’ P)
In mathematics, it is very common for there to be multiple ways to solve a given a problem; the same can be said of logic. There is often a variety of ways to perform a natural deduction. Now, construct an alternate proof. In other words, if the proof was done using RAA, now use CP; if you used CP, now use RAA. Consider the following questions, as well, in your journal response:
•Will a direct proof work for any of these?
•Can the proof be performed more efficiently by using different equivalence rules?

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