document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=76567>Question 76567</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given: (~ p &#8594; q) &#8744; ~ p<BR>\n" );
document.write( "This statement is a:<BR>\n" );
document.write( "A. Biconditional statement B. Self-Contradiction<BR>\n" );
document.write( "C. Tautology D. Conjunction </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54912 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=54912\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we let p be false, then the entire disjunction is true since we would have\r<BR>\n" );
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document.write( "(~(false) &#8594; q) &#8744; ~ (false)\r<BR>\n" );
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document.write( "(true &#8594; q) &#8744; true\r<BR>\n" );
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document.write( "We can see that a disjunction is true if either side is true. Since the left side is true, the entire disjunction is true.\r<BR>\n" );
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document.write( "If we let p be true, then the entire disjunction is also true since we would have\r<BR>\n" );
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document.write( "(~(true) &#8594; q) &#8744; ~ (true)\r<BR>\n" );
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document.write( "(false &#8594; q) &#8744; false\r<BR>\n" );
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document.write( "Since a false antecedent means the entire implication is true, the whole left disjunct is true. This means the whole disjunction is true. So for any p (in this case q can be anything), the logical statement is true. This means the statement is a tautology (answer c). </SPAN>\n" );
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