# Using the 18 Rules of Natural Deduction in Proofs

* 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

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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