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

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) (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.

Number	Statement	Lines Used	Reason
1	~N -> (~R -> C)
2	R -> N
3	~C
:.	N
4	(~N & ~R) -> C	1	Exportation
5	~(~N & ~R)	4,3	Modus Tollens
6	~~N v ~~R	5	De Morgan’s Law
7	~~N v R	6	Double Negation
8	~N -> R	7	Material Implication
9	~N -> N	8,2	Hypothetical Syllogism
10	~~N v N	9	Material Implication
11	N v N	10	Double Negation
12	N	11	Tautology

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