Using all 18 rules in natural deduction to answer 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

© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/philosophy/logic-critical-thinking/using-all-18-rules-in-natural-deduction-to-answer-proofs-1gj

Solution Preview

...n
6. (A * B) > C 3 Exportation
7. ~C Assumption
8. ~(A * B) 6, 7 Modus Tollens
9. ~~A * ~~B 2 DeMorgans
10. A * B 9 Double Negation (teice)
11. (A * B) * ~(A * B) 8, 10 Conjunction
12. ~~C 7-11 Indirect Proof
13. C 12 Double Negation

1. M*T
2. .(M*D)>K
3. (K*T)>~D /~D
4. D Assumption
5. ~~D 4 Double Negation
6. ~(K ...