document.write( "Question 1198762: Use Indirect proof to solve the following:\r
\n" ); document.write( "\n" ); document.write( "(P v F) ⊃ (A v D)
\n" ); document.write( "A ⊃ (M • ~P)
\n" ); document.write( "D ⊃ (C • ~P) / ~P \n" ); document.write( "

Algebra.Com's Answer #832396 by math_tutor2020(3817) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "This is one way to do the derivation.
\n" ); document.write( "\n" ); document.write( "\n" ); document.write( "

Number		Statement	Line(s) Used	Reason
1		(P v F) ⊃ (A v D)
2		A ⊃ (M • ~P)
3		D ⊃ (C • ~P)
:.		~P
	4	~(~P)		Assumption For Indirect Proof
	5	P	4	Double Negation
	6	P v F	5	Addition
	7	A v D	1,6	Modus Ponens
	8	(M • ~P) v (C • ~P)	2,3,7	Constructive Dilemma
	9	(M v C) • ~P	8	Distribution
	10	~P	9	Simplification
	11	~P • P	10,5	Conjunction
12		~P	4 - 11	Indirect Proof

\n" ); document.write( "The idea is to start with the conclusion ~P and negate it to get ~(~P).
\n" ); document.write( "The goal is to show a contradiction arises when we assume the opposite of the conclusion.
\n" ); document.write( "As shown above, the contradiction happens on line 11 when we have ~P and P together.
\n" ); document.write( "This contradiction then leads us to conclude the opposite of the assumption ~(~P) must be the case, i.e. the original conclusion we started with is the case.
\n" ); document.write( "This fully wraps up the proof.
\n" ); document.write( " \n" ); document.write( "

\n" );