SOLUTION: Use an ordinary proof (not conditional or indirect proof): 1. ∼N ⊃ (∼R ⊃ C) 2. R ⊃ N 3. ∼C / N

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Question 1169573: Use an ordinary proof (not conditional or indirect proof):

1. ∼N ⊃ (∼R ⊃ C)
2. R ⊃ N
3. ∼C / N
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!
Here's one way to do the derivation. I'm using arrow symbols in place of horseshoe symbols.

NumberStatementLines UsedReason
1~N -> (~R -> C)
2R -> N
3~C
:.N
4(~N & ~R) -> C1Exportation
5~(~N & ~R)4,3Modus Tollens
6~~N v ~~R5De Morgan’s Law
7~~N v R6Double Negation
8~N -> R7Material Implication
9~N -> N8,2Hypothetical Syllogism
10~~N v N9Material Implication
11N v N10Double Negation
12N11Tautology