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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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Solution Summary

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

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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 ...

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