document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179563>Question 1179563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I could really use some help. Thank You<BR>\n" );
document.write( "INSTRUCTIONS: Use natural deduction to derive the conclusion in each problem.<BR>\n" );
document.write( "Prove this using natural deduction.<BR>\n" );
document.write( "NOTE: Use * for dot, v for wedge, ~ for tilde, = for triple bar (or copy and paste ≡), and > for horseshoe (or copy and paste ⊃ )\r<BR>\n" );
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document.write( "1.	N  ≡  F	 <BR>\n" );
document.write( "2.	~F v ~N	 <BR>\n" );
document.write( "3.	D ⊃ N	/~(F v D)<BR>\n" );
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document.write( "1.	M ⊃ (∼B ⊃ J)	 <BR>\n" );
document.write( "2.	B ⊃ (~M * ~M)	 <BR>\n" );
document.write( "3.	∼J	/ ~M<BR>\n" );
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document.write( "1.	~X ⊃ ~~O	 <BR>\n" );
document.write( "2.	~X ⊃ A	 <BR>\n" );
document.write( "3.	~(O * A)    / X </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850219 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850219\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **Problem 1:**\r<BR>\n" );
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document.write( "1. N ≡ F  (Given)<BR>\n" );
document.write( "2. ~F v ~N  (Given)<BR>\n" );
document.write( "3. D ⊃ N  (Given)<BR>\n" );
document.write( "4. | F v D  (Assumption for Indirect Proof)<BR>\n" );
document.write( "5. | | F  (Assumption for v Elimination)<BR>\n" );
document.write( "6. | | N  (1, 5, ≡ Elimination)<BR>\n" );
document.write( "7. | | N v ~D  (6, v Introduction)<BR>\n" );
document.write( "8. | | ~D  (2, 7, v Elimination)<BR>\n" );
document.write( "9. | | F ⊃ ~D  (5, 8, ⊃ Introduction)<BR>\n" );
document.write( "10. | | D  (Assumption for v Elimination)<BR>\n" );
document.write( "11. | | N  (3, 10, ⊃ Elimination)<BR>\n" );
document.write( "12. | | N v ~D  (11, v Introduction)<BR>\n" );
document.write( "13. | | ~D  (2, 12, v Elimination)<BR>\n" );
document.write( "14. | | D ⊃ ~D  (10, 13, ⊃ Introduction)<BR>\n" );
document.write( "15. | | ~D v ~D  (4, 9, 14, v Elimination)<BR>\n" );
document.write( "16. | | ~D  (15, Tautology)<BR>\n" );
document.write( "17. | ~(F v D)  (4, 16, ⊃ Introduction) \r<BR>\n" );
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document.write( "**Problem 2:**\r<BR>\n" );
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document.write( "1. M ⊃ (∼B ⊃ J)  (Given)<BR>\n" );
document.write( "2. B ⊃ (~M * ~M)  (Given)<BR>\n" );
document.write( "3. ∼J  (Given)<BR>\n" );
document.write( "4. | M  (Assumption for Indirect Proof)<BR>\n" );
document.write( "5. | | ∼B  (Assumption for Indirect Proof) <BR>\n" );
document.write( "6. | | ∼B ⊃ J (1, 4, ⊃ Elimination)<BR>\n" );
document.write( "7. | | J  (5, 6, ⊃ Elimination)<BR>\n" );
document.write( "8. | | J * ~J  (3, 7, * Introduction)<BR>\n" );
document.write( "9. | B  (5, 8, ~ Introduction)<BR>\n" );
document.write( "10. | ~M * ~M  (2, 9, ⊃ Elimination)<BR>\n" );
document.write( "11. | ~M  (10, * Elimination)<BR>\n" );
document.write( "12. | M * ~M  (4, 11, * Introduction)<BR>\n" );
document.write( "13. ~M  (4, 12, ~ Introduction)\r<BR>\n" );
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document.write( "**Problem 3:**\r<BR>\n" );
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document.write( "1. ~X ⊃ ~~O  (Given)<BR>\n" );
document.write( "2. ~X ⊃ A  (Given)<BR>\n" );
document.write( "3. ~(O * A)  (Given)<BR>\n" );
document.write( "4. | ~X  (Assumption for Indirect Proof)<BR>\n" );
document.write( "5. | ~~O  (1, 4, ⊃ Elimination)<BR>\n" );
document.write( "6. | O  (5, ~~ Elimination)<BR>\n" );
document.write( "7. | A  (2, 4, ⊃ Elimination)<BR>\n" );
document.write( "8. | O * A  (6, 7, * Introduction)<BR>\n" );
document.write( "9. | (O * A) * ~(O * A)  (3, 8, * Introduction)<BR>\n" );
document.write( "10. X  (4, 9, ~ Introduction) </SPAN>\n" );
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