document.write( "Question 1029291: Hi! I really could use some help solving these two proofs below. I also included instructions! \r
\n" ); document.write( "\n" ); document.write( "Instructions: You must construct a proof for two of the following. All proofs include at least 4 steps (besides the original premises). \r
\n" ); document.write( "\n" ); document.write( "I have left the section and problem numbers so that you can check your answers online before posting them. Here is the website for checking your answers:\r
\n" ); document.write( "\n" ); document.write( "http://www.poweroflogic.com/cgi/menu.cgi\r
\n" ); document.write( "\n" ); document.write( "You can expand the readable area to show the whole argument by clicking and dragging on the triangle shape at the bottom right of this area.\r
\n" ); document.write( "\n" ); document.write( "Questions from The Power of Logic 5th Edition/Chapter 8/Section 8.3/Part C\r
\n" ); document.write( "\n" ); document.write( "15. (~D v E) • (~D v ~F), (E • ~F) → ~G, ~D → ~G ∴ ~G
\n" ); document.write( "24. ~O ∴ ~Q → ~(O • P)\r
\n" ); document.write( "\n" ); document.write( "Please & Thank you :) \n" ); document.write( "

Algebra.Com's Answer #644349 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Problem #15\r
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Number	Statement	Lines Used	Reason
1	(~D v E) & (~D v ~F)
2	(E & ~F) -> ~G
3	~D -> ~G
:.	~G
4	~D v E	1	Simp
5	~D v ~F	1	Simp
6	D -> E	4	MI
7	D -> ~F	5	MI
8	E -> (~F -> ~G)	2	Exp
9	D -> (~F -> ~G)	6,8	HS
10	(D & ~F) -> ~G	9	Exp
11	(~F & D) -> ~G	10	Comm
12	~F -> (D -> ~G)	11	Exp
13	D - > (D -> ~G)	7,12	HS
14	(D & D) -> ~G	13	Exp
15	D -> ~G	14	Taut
16	G -> D	3	Trans
17	G -> ~G	16,15	HS
18	~G v ~G	17	MI
19	~G	18	Taut

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\n" ); document.write( "\n" ); document.write( "Abbreviations Used:\r
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\n" ); document.write( "\n" ); document.write( "Comm: Commutation
\n" ); document.write( "Exp: Exportation
\n" ); document.write( "HS: Hypothetical Syllogism
\n" ); document.write( "MI: Material Implication
\n" ); document.write( "Simp: Simplification
\n" ); document.write( "Taut: Tautology
\n" ); document.write( "Trans: Transposition\r
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\n" ); document.write( "\n" ); document.write( "Problem #24\r
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Number	Statement	Lines Used	Reason
1	~O
:.	~Q -> ~(O & P)
2	~O v Q	1	Add
3	Q v ~O	2	Comm
4	(Q v ~O) v ~P	3	Add
5	~(~Q & O) v ~P	4	DM
6	(~Q & O) -> ~P	5	MI
7	~Q -> (O -> ~P)	6	Exp
8	~Q -> (~O v ~P)	7	MI
9	~Q -> ~(O & P)	8	DM

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\n" ); document.write( "\n" ); document.write( "Abbreviations Used:\r
\n" ); document.write( "\n" ); document.write( "Add: Addition
\n" ); document.write( "Comm: Commutation
\n" ); document.write( "DM: De Morgan's Law
\n" ); document.write( "Exp: Exportation
\n" ); document.write( "MI: Material Implication \n" ); document.write( "

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