document.write( "Question 1005236: F > ~G
\n" ); document.write( "~F > (H > ~G)
\n" ); document.write( "(~I v ~H) > ~~G
\n" ); document.write( "~I
\n" ); document.write( "/ ~H \n" ); document.write( "

Algebra.Com's Answer #621565 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
\n" ); document.write( "\n" ); document.write( "

Number	Statement	Lines Used	Reason
1	F > ~G
2	~F > (H > ~G)
3	(~I v ~H) > ~~G
4	~I
:.	~H
5	(~I v ~H) > G	3	DN
6	~(~I v ~H) v G	5	MI
7	(~~I * ~~H) v G	6	DM
8	(I * H) v G	7	DN
9	G v (I * H)	8	Comm
10	(G v I) * (G v H)	9	Dist
11	G v I	10	Simp
12	I v G	11	Comm
13	G	12,4	DS
14	~~G	13	DN
15	~F	1,14	MT
16	H > ~G	2,15	MP
17	~H	16,14	MT

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Abbreviation/Acronyms Used\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Comm = Commutation
\n" ); document.write( "Dist = Distribution
\n" ); document.write( "DM = De Morgan's Law
\n" ); document.write( "DN = Double Negation
\n" ); document.write( "DS = Disjunctive Syllogism
\n" ); document.write( "MI = Material Implication
\n" ); document.write( "MP = Modus Ponens
\n" ); document.write( "MT = Modus Tollens
\n" ); document.write( "Simp = Simplification \n" ); document.write( "

\n" );