document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201675>Question 1201675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use rules of implication to derive the indicated conclusions.\r<BR>\n" );
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document.write( "1. R ⊃ (G v ~A) 2. (G v ~A) ⊃ ~S 3. G ⊃ S 4. R/~A\r<BR>\n" );
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document.write( "1. ~N⊃ [(B ⊃ D) ⊃(N v~E)] 2. (B ⊃ E) ⊃ ~N 3. B ⊃ D 4. D ⊃ E / ~D\r<BR>\n" );
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document.write( "1. ~M ⊃ Q 2. R ⊃ ~T 3. ~M v R / Q v ~T  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836153 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=836153\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll do problem 1 to get you started.\r<BR>\n" );
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document.write( "This is what the 1st question looks like when each premise gets its own line.<BR>\n" );
document.write( "1. R ⊃ (G v ~A) <BR>\n" );
document.write( "2. (G v ~A) ⊃ ~S <BR>\n" );
document.write( "3. G ⊃ S <BR>\n" );
document.write( "4. R<BR>\n" );
document.write( ":. ~A\r<BR>\n" );
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document.write( "Here is one way to do the derivation.<BR>\n" );
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document.write( "<tr><TD >Number</TD><TD >Statement</TD><TD >Lines Used</TD><TD >Reason</TD></tr><tr><TD >1</TD><TD >R -> (G v ~A)</TD><TD ></TD><TD ></TD></tr><tr><TD >2</TD><TD >(G v ~A) -> ~S</TD><TD ></TD><TD ></TD></tr><tr><TD >3</TD><TD >G -> S</TD><TD ></TD><TD ></TD></tr><tr><TD >4</TD><TD >R</TD><TD ></TD><TD ></TD></tr><tr><TD >:.</TD><TD >~A</TD><TD ></TD><TD ></TD></tr><tr><TD >5</TD><TD >R -> ~S</TD><TD >1,2</TD><TD >Hypothetical Syllogism</TD></tr><tr><TD >6</TD><TD >~S</TD><TD >5,4</TD><TD >Modus Ponens</TD></tr><tr><TD >7</TD><TD >G v ~A</TD><TD >1,4</TD><TD >Modus Ponens</TD></tr><tr><TD >8</TD><TD >~G</TD><TD >3,6</TD><TD >Modus Tollens</TD></tr><tr><TD >9</TD><TD >~A</TD><TD >7,8</TD><TD >Disjunctive Syllogism</TD></tr>\n" );
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document.write( "I used arrows in place of the horseshoe symbols.\r<BR>\n" );
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document.write( "For more information, check out the various rules of inference and rules of replacement as shown in the link below.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://logiccurriculum.com/2019/02/09/rules-for-proofs/\">https://logiccurriculum.com/2019/02/09/rules-for-proofs/</a>\r<BR>\n" );
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document.write( "Similar logic questions<BR>\n" );
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document.write( "</font> </SPAN>\n" );
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