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# Construct proofs for given valid arguments using the eight rules of inference.

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Using the eight rules of inference (Simplication, Conjunction, Addition, Constructive Dilemma, Modus Ponens, Modus Tollens, Disjunctive Syllogism and Hypothetical Syllogism), construct a proof for each of the following valid arguments.

A)
1. (C & ~E) > (E v T) ------- Premise
2. C ------- Premise
3. ~E / T ------- Premise / Conclusion

B)
1. (R v P) > (G v M) ------- Premise
2. R & U ------- Premise
3. (G > E) & (M > F) ------- Premise
4. (E v F) > C / C ------- Premise / Conclusion

C)
1. (P v S) > (L > R) & (I > M) ------- Premise
2. (P v N) > (L v I) ------- Premise
3. (P & W) / (R v M) ------- Premise / Conclusion

https://brainmass.com/math/logic/construct-proofs-using-the-eight-rules-of-inference-630984

#### Solution Preview

[A]
1. (C & ~E) > (E v T) ... [Premise]
2. C ... [Premise]
3. ~E ... [Premise]

4. (C & ~E) ... [Conjunction on 2 and 3]
5. (E v T) ... [Modus Ponens on 1 and 4]
6. T ... [Disjunctive Syllogism on 3 and 5; Conclusion]

[B]
1. (R v P) > (G v M) ... [Premise]
2. R & U ...

#### Solution Summary

Solution uses the eight rules of inference to find a proof leading to conclusion, explaining how a step was arrived from using premises/results from earlier steps.

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