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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 Ã¢â‚¬Â¢ P) Ã¢â€ â€™ K, E Ã¢â€ â€™ Z, ~P Ã¢â€ â€™ ~ Z, G Ã¢â€ â€™ (E v L), therefore, (G Ã¢â‚¬Â¢ ~L) Ã¢â€ â€™ K
(S v T) v E, S Ã¢â€ â€™ (F Ã¢â‚¬Â¢ ~G), A Ã¢â€ â€™ W, T Ã¢â€ â€™ ~W, therefore, (~E Ã¢â‚¬Â¢ A) Ã¢â€ â€™ ~G
(S v T) v (U v W), therefore, (U v T) v (S v W)
~Q Ã¢â€ â€™ (L Ã¢â€ â€™ F), Q Ã¢â€ â€™ ~A, F Ã¢â€ â€™ B, L, therefore, ~A v B
~S Ã¢â€ â€™ (F Ã¢â€ â€™ L), F Ã¢â€ â€™ (L Ã¢â€ â€™ P), therefore, ~S Ã¢â€ â€™ (F Ã¢â€ â€™ 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. In your peer responses, make suggestions for an alternate proof. Consider the following questions when constructing your response:
If the proof was done using RAA, could it be done using CP? What about vice versa?
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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