document.write( "Question 1008772: 1. (R v S) > (H & ~G)
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Algebra.Com's Answer #624355 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Proof by contradiction\r
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Number	Statement	Lines Used	Reason
1		(R v S) -> (H & ~G)
2		(K v R) -> (G v ~H)
.:		~R
	3	~~R		AIP
	4	R	3	DN
	5	R v S	4	Add
	6	R v K	4	Add
	7	K v R	6	Comm
	8	H & ~G	1,5	MP
	9	~G & H	8	Comm
	10	H	8	Simp
	11	~G	9	Simp
	12	G v ~H	2,7	MP
	13	~H	12,11	DS
	14	H & ~H	10,13	Conj
15		~(~~R)	3-14	IP
16		~R	15	DN

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\n" ); document.write( "\n" ); document.write( "Acronyms/Abbreviations Used\r
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\n" ); document.write( "\n" ); document.write( "Add = Addition
\n" ); document.write( "AIP = Assumption for Indirect Proof
\n" ); document.write( "Comm = Commutation
\n" ); document.write( "Conj = Conjunction
\n" ); document.write( "DM = De Morgan's Law
\n" ); document.write( "DN = Double Negation
\n" ); document.write( "DS = Disjunctive Syllogism
\n" ); document.write( "IP = Indirect Proof (aka proof by contradiction)
\n" ); document.write( "MP = Modus Ponens
\n" ); document.write( "Simp = Simplification \n" ); document.write( "

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