document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201697>Question 1201697</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Is the rule of conjunction like this example true? P v Q<BR>\n" );
document.write( "Q v P<BR>\n" );
document.write( "(P v Q) · (Q v P)\r<BR>\n" );
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document.write( "Is this example a disjunctive syllogism? P v Q\r<BR>\n" );
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document.write( "	~Q__<BR>\n" );
document.write( "          ~P<BR>\n" );
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document.write( "The last question I need help on is this a simplication proof example A v B<BR>\n" );
document.write( "A<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836356 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</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=836356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Refer to rules 4, 5, 7, and 9.<BR>\n" );
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document.write( "Image Source:<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><BR>\n" );
document.write( "That page goes over the various logic rules of inference and rules of replacement.<BR>\n" );
document.write( "The screenshot shown above focuses on the rules of inference specifically.\r<BR>\n" );
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document.write( "We cannot use rule 9 (addition) in reverse.<BR>\n" );
document.write( "We cannot go from \"P v Q\" to \"P\".<BR>\n" );
document.write( "However, rule 5 (conjunction) does work in reverse (to get rule 7 simplification).\r<BR>\n" );
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document.write( "Further Reading<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.tutorialspoint.com/discrete_mathematics/rules_of_inference.htm\">https://www.tutorialspoint.com/discrete_mathematics/rules_of_inference.htm</a><BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/2%3A_Logic/2.6_Arguments_and_Rules_of_Inference\">https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/2%3A_Logic/2.6_Arguments_and_Rules_of_Inference</a><BR>\n" );
document.write( "The second link refers to \"Elimination\", which is really \"Disjunctive Syllogism\" by another name.<BR>\n" );
document.write( "Also, that second link talks about \"Transitivity\" aka \"Hypothetical Syllogism\". <BR>\n" );
document.write( "There are probably other examples of rules going by multiple names. <BR>\n" );
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