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    Using the 18 Rules of Natural Deduction in Proofs

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    * represents dot and > represents horse shoe

    #1
    1. Av(B*C)
    2. A>B / B

    #2
    1.A=B
    2.AvB
    3.A>(B>C) /C

    #3
    1. M*T
    2.(M*D)>K
    3.(K*T)>~D /~D

    #4
    1.(A*B)>(C*D)
    2.(DV~A)> E*F
    3.~F /~B

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    https://brainmass.com/philosophy/logic-critical-thinking/rules-natural-deduction-proofs-1555

    Solution Preview

    Please see the attached file

    1. A v (B*C)
    2. A>B / B
    3. ~B Assumption
    4. ~A 2, 3 Modus Tollens
    5. B * C 1, 4 Disjunctive Syllogism
    6. B 5 Simplification
    7. B * ~B 6, 3 Conjunction
    8. ~~B 3-7 Indirect Proof
    9. B 8 Double Negation

    1. A=B
    2. A v B
    3. A>(B>C) /C
    4. (A > B) * (B > A) 1 Equivalence
    5. A > B 4 ...

    Solution Summary

    The 18 rules in natural deduction to answer proofs is examined. The proofs are analyzed.

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