document.write( "Question 1009929: Natural Deduction - all 18 rules can be used\r
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Algebra.Com's Answer #625429 by jim_thompson5910(35256) $\"\"$ $\"About$

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Natural Deduction\r
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Number	Statement	Lines Used	Reason
1	M -> (R ^ E)
2	(E v H) -> G
:.	M -> G
3	~(E v H) v G	2	MI
4	(~E ^ ~H) v G	3	DM
5	G v (~E ^ ~H)	4	Comm
6	(G v ~E) ^ (G v ~H)	5	Dist
7	G v ~E	6	Simp
8	~E v G	7	Comm
9	E -> G	8	MI
10	~M v (R ^ E)	1	MI
11	(~M v R) ^ (~M v E)	10	Dist
12	(~M v E) ^ (~M v R)	11	Comm
13	~M v E	21	Simp
14	M -> E	13	MI
15	M -> G	14,9	HS

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\n" ); document.write( "\n" ); document.write( "Conditional Proof (alternative method)\r
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\n" ); document.write( "\n" ); document.write( "Assume M is true. Show this leads to G being true.\r
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Number	Statement	Lines Used	Reason
1		M -> (R ^ E)
2		(E v H) -> G
:.		M -> G
	3	M		ACP
	4	R ^ E	1,3	MP
	5	E ^ R	4	Comm
	6	E	5	Simp
	7	E v H	6	Add
	8	G	2,7	MP
9		M -> G	3-8	CP

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\n" ); document.write( "\n" ); document.write( "Abbreviations/Acronyms Used (applies to either method)\r
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\n" ); document.write( "\n" ); document.write( "ACP = Assumption for Conditional Proof
\n" ); document.write( "Add = Addition
\n" ); document.write( "Comm = Commutation
\n" ); document.write( "CP = Conditional Proof
\n" ); document.write( "Dist = Distribution
\n" ); document.write( "DM = De Morgan's Law
\n" ); document.write( "HS = Hypothetical Syllogism
\n" ); document.write( "MI = Material Implication
\n" ); document.write( "MP = Modus Ponens
\n" ); document.write( "Simp = Simplification \n" ); document.write( "

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