document.write( "Question 1169573: Use an ordinary proof (not conditional or indirect proof):
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "1. ∼N ⊃ (∼R ⊃ C)
\n" ); document.write( "2. R ⊃ N
\n" ); document.write( "3. ∼C / N \n" ); document.write( "

Algebra.Com's Answer #794383 by math_tutor2020(3817) $\"\"$ $\"About$

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. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

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

\n" ); document.write( " \n" ); document.write( "

\n" );