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

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.