Explore BrainMass
Share

Explore BrainMass

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

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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

    © BrainMass Inc. brainmass.com October 10, 2019, 8:31 am ad1c9bdddf
    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.

    $2.19