document.write( "Question 1009334: Derive: A v ~B
\n" ); document.write( "1.(F v G) v (A v ~B)
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Algebra.Com's Answer #624873 by jim_thompson5910(35256) $\"\"$ $\"About$

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Proof by contradiction\r
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Number	Statement	Lines Used	Reason
1		(F v G) v (A v ~B)
2		F -> A
3		B -> ~G
.:		A v ~B
	5	~(A v ~B)		AIP
	6	~A & ~~B	5	DM
	7	~A & B	6	DN
	8	B & ~A	7	Comm
	9	~A	7	Simp
	10	B	8	Simp
	11	~F	2,9	MT
	12	~G	3,10	MP
	13	~F & ~G	11,12	Conj
	14	~(F v G)	13	DM
	15	A v ~B	1,14	DS
	16	~B	15,9	DS
	17	B & ~B	10,16	Conj
18		A v ~B	5-17	IP

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\n" ); document.write( "\n" ); document.write( "Acroynyms/Abbreviations used\r
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\n" ); document.write( "\n" ); document.write( "AIP = assumption for indirect proof
\n" ); document.write( "Comm = commutation
\n" ); document.write( "Conj = conjunction
\n" ); document.write( "IP = indirect proof
\n" ); document.write( "DM = de morgan's law
\n" ); document.write( "DN = double negation
\n" ); document.write( "DS = disjunctive syllogism
\n" ); document.write( "MP = modus ponens
\n" ); document.write( "MT = modus tollens
\n" ); document.write( "Simp = simplification \n" ); document.write( "

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