document.write( "Question 1004972: I need help deriving the conclusion (using CONDITIONAL proof). You can use all 18 rules.\r
\n" ); document.write( "\n" ); document.write( "1. (AvB)⊃(CvD)
\n" ); document.write( "2. (CvE)⊃D /A⊃D \n" ); document.write( "

Algebra.Com's Answer #621310 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Note: I'm going to use the symbol -> in place of the horseshoe symbol.\r
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Number		Statement	Lines Used	Reason
1		(A v B) -> (C v D)
2		(C v E) -> D
:.		A -> D
\|	3	A		ACP
\|	4	A v B	3	Add
\|	5	C v D	1,4	MP
\|	6	D v C	5	Comm
\|	7	~~D v C	6	DN
\|	8	~D -> C	7	MI
\|	9	~(C v E) v D	2	MI
\|	10	(~C * ~E) v D	9	DM
\|	11	D v (~C * ~E)	10	Comm
\|	12	(D v ~C) * (D v ~E)	11	Dist
\|	13	D v ~C	12	Simp
\|	14	~C v D	13	Comm
\|	15	C -> D	14	MI
\|	16	~D -> D	8,15	HS
\|	17	~~D v D	16	MI
\|	18	D v D	17	DN
\|	19	D	18	Taut
20		A -> D	3-19	CP

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\n" ); document.write( "\n" ); document.write( "Abbreviations/Acronyms Used\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( "DN = Double Negation
\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( "Taut = Tautology \n" ); document.write( "

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