document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061923>Question 1061923</A>: <I><SPAN STYLE=\"word-break: break-all;\"> looking for help on why the argument is or is not valid on  these two.  Can anyone help me out...thanks in advance. Validity of each argument\r<BR>\n" );
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document.write( "For the first problem I began with ( p U q) u r<BR>\n" );
document.write( "                                    P'U Q<BR>\n" );
document.write( "                                    ________<BR>\n" );
document.write( "                                     R\r<BR>\n" );
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document.write( "( p v q ) &#8594; r<BR>\n" );
document.write( "~ p &#8594; q<BR>\n" );
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document.write( "r\r<BR>\n" );
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document.write( "( p &#8594; q) &#8594;r<BR>\n" );
document.write( "~p v q <BR>\n" );
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document.write( "r V q\r<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 #676702 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=676702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "For the first one, Material Implication says that p V q is equivalent to ~p -> q.   So you can simply replace one expression with the other and then the conclusion is true by Modus Ponens.\r<BR>\n" );
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document.write( "The second one is true for the same reason.  p -> q is equivalent to ~p V q, again by Material Implication.\r<BR>\n" );
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document.write( "See: <a  rel=nofollow HREF=\"https://en.wikipedia.org/wiki/Material_implication_(rule_of_inference)\">Material Implication</a>\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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