document.write( "Question 1060204: Using an indirect proof to solve this problem:\r
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Algebra.Com's Answer #675232 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
The idea is to assume the complete opposite of the conclusion (statement 3). \r
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\n" ); document.write( "\n" ); document.write( "This contradiction means that the opposite of the assumption must be true. In other words, the original conclusion is true. \r
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Number	Statement	Lines Used	Reason
1		B -> (C -> ~B)
2		A -> (B -> C)
:.		~A v ~B
	3	~(~A v ~B)		AIP
	4	~~A & ~~B	3	DM
	5	A & B	4	DN
	6	B & A	5	Comm
	7	A	5	Simp
	8	B	6	Simp
	9	C -> ~B	1,8	MP
	10	B -> C	2,7	MP
	11	B -> ~B	10,9	HS
	12	~B v ~B	11	MI
	13	~B	12	Taut
	14	B & ~B	8,13	Conj
15		~A v ~B	3-14	IP

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\n" ); document.write( "\n" ); document.write( "Abbreviations/Acronyms Used\r
\n" ); document.write( "\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( "HS = Hypothetical Syllogism
\n" ); document.write( "IP = Indirect Proof
\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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