SOLUTION: Use natural deduction to derive the conclusion in each problem. Use an ordinary proof (not conditional or indirect proof): 1. (O ⊃ C) • (∼S ⊃ ∼D) 2. (E ⊃

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Question 1156932: Use natural deduction to derive the conclusion in each problem.

Use an ordinary proof (not conditional or indirect proof):

1. (O ⊃ C) • (∼S ⊃ ∼D)
2. (E ⊃ D) • (∼E ⊃ ∼C) / O ⊃ S
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
1.	(O ⊃ C) • (∼S ⊃ ∼D)	 
2.	(E ⊃ D) • (∼E ⊃ ∼C)	 / O ⊃ S

3.       O ⊃ C                 1, Simplification
4.      (∼E ⊃ ∼C) • (E ⊃ D)   2, Commutation
5.       ∼E ⊃ ∼C              4, Simplification
6.       ∼∼C ⊃ ∼∼E            5, Transposition
7.       C ⊃ E                 6, Double Negation
8.       O ⊃ E                 3,7, Hypothetical Syllogism
9.       E ⊃ D                 2, Simplification
10.      O ⊃ D                 8,9, Hypothetical Syllogism
11.     (∼S ⊃ ∼D) • (O ⊃ C)   1, Commutation
12.      ∼S ⊃ ∼D              11, Simplification
13.      ∼∼D ⊃ ∼∼S            12, Transposition
14.      D ⊃ S                 13, Double Negation
15.      O ⊃ S                 10,14, Hypothetical Syllogism

Edwin
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