document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1032455>Question 1032455</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that the following 4 logical propositions are all true :<BR>\n" );
document.write( "1. A &#8594; B<BR>\n" );
document.write( "2. C &#8594; D<BR>\n" );
document.write( "3. A &#8744; C<BR>\n" );
document.write( "4. ŹD<BR>\n" );
document.write( "What can you say about the truth value of propositions A, B, C and D. You<BR>\n" );
document.write( "can answer true, false, or uncertain. Justify your answers.<BR>\n" );
document.write( "Truth value of proposition D :<BR>\n" );
document.write( "Truth value of proposition C :<BR>\n" );
document.write( "Truth value of proposition A :<BR>\n" );
document.write( "Truth value of proposition B :<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 #647127 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=647127\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=blue>ŹD</font> is given to be true (premise 4). So the opposite of that, D, must be false.\r<BR>\n" );
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document.write( "Truth value of proposition D : <font color = red>false</font>\r<BR>\n" );
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document.write( "If D is false, then <font color=blue>C -> D</font> would be false if C were true. Since implications are false if the antecedent is true while the conclusion is false. \r<BR>\n" );
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document.write( "But we're given <font color=blue>C -> D</font> to be true. This forces C to be false\r<BR>\n" );
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document.write( "Truth value of proposition C : <font color = red>false</font>\r<BR>\n" );
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document.write( "In premise 3, <font color=blue>A v C</font> is assumed to be true. So either A is true or C is true.\r<BR>\n" );
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document.write( "Now that we know that C is false, we conclude that A must be true to make <font color=blue>A v C</font> true\r<BR>\n" );
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document.write( "Truth value of proposition A : <font color = red>true</font>\r<BR>\n" );
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document.write( "<font color=blue>A -> B</font> is true (assumption; premise 1)\r<BR>\n" );
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document.write( "A is true (see last section above)<BR>\n" );
document.write( "To ensure that <font color=blue>A -> B</font> is true, we must force B to be true as well. If B were false, then <font color=blue>A -> B</font> would be false. \r<BR>\n" );
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document.write( "Truth value of proposition B : <font color = red>true</font>\r<BR>\n" );
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document.write( "Summary:\r<BR>\n" );
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document.write( "Truth value of proposition D : <font color = red>false</font><BR>\n" );
document.write( "Truth value of proposition C : <font color = red>false</font><BR>\n" );
document.write( "Truth value of proposition A : <font color = red>true</font><BR>\n" );
document.write( "Truth value of proposition B : <font color = red>true</font> </SPAN>\n" );
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