document.write( "Question 1208773: Premise:
\n" ); document.write( "1.
\n" ); document.write( "(L ≡ N) ⊃ C
\n" ); document.write( "2.
\n" ); document.write( "(L ≡ N) ∨ (P ⊃ ~E)
\n" ); document.write( "3.
\n" ); document.write( "~E ⊃ C
\n" ); document.write( "4.
\n" ); document.write( "~C
\n" ); document.write( "Conclusion:
\n" ); document.write( "~P\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "I need the proof but im struggling \n" ); document.write( "

Algebra.Com's Answer #847229 by math_tutor2020(3816) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "

\r\n" );
document.write( "Premise:\r\n" );
document.write( "1. (L ≡ N) ⊃ C\r\n" );
document.write( "2. (L ≡ N) ∨ (P ⊃ ~E)\r\n" );
document.write( "3. ~E ⊃ C\r\n" );
document.write( "4. ~C\r\n" );
document.write( "Conclusion: ~P\r\n" );
document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Here is one way to do the derivation. There may be other approaches.
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

Number	Statement	Line(s) Used	Reason
1	(L ≡ N) ⊃ C
2	(L ≡ N) v (P ⊃ ~E)
3	~E ⊃ C
4	~C
:.	~P
5	~(L ≡ N)	1,4	Modus Tollens
6	P ⊃ ~E	2,5	Disjunctive Syllogism
7	~(~E)	3,4	Modus Tollens
8	E	7	Double Negation
9	~P	6,8	Modus Tollens

\n" ); document.write( "Here's a list of rules of inference and replacement
\n" ); document.write( " \n" ); document.write( "

\n" );