document.write( "Question 1031401: ∼A∙~B
\n" ); document.write( "~D⊃A
\n" ); document.write( "M⊃[(NvO)⊃P]
\n" ); document.write( "Q⊃(SvT)
\n" ); document.write( "(~Qv~R)⊃(M∙N)
\n" ); document.write( "~Dv~(SvT) ∴P∙~B \n" ); document.write( "

Algebra.Com's Answer #646094 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	~A & ~B
2	~D -> A
3	M -> [(N v O) -> P]
4	Q -> (S v T)
5	(~Q v ~R) -> (M & N)
6	~D v ~(S v T)
:.	P & ~B
7	~B & ~A	1	Commutation
8	~A	1	Simplification
9	~B	7	Simplification
10	~~D	2,8	Modus Tollens
11	~(S v T)	6,10	Disjunctive Syllogism
12	~Q	4,11	Modus Tollens
13	~Q v ~R	12	Addition
14	M & N	5,13	Modus Ponens
15	N & M	14	Commutation
16	M	14	Simplification
17	N	15	Simplification
18	N v O	17	Addition
19	(N v O) -> P	3,16	Modus Ponens
20	P	19,18	Modus Ponens
21	P & ~B	20,9	Conjunction

\n" ); document.write( "

\n" );