document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205226>Question 1205226</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use natural deduction to derive the conclusion in each problem.\r<BR>\n" );
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document.write( "Use natural deduction to prove the following logical truth:<BR>\n" );
document.write( "(P ⊃ Q) ≡ [P ⊃ (Q ∨ ∼P)] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842199 by </B><A HREF=/tutors/aboutme.mpl?userid=Bogz><B>Bogz(13)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Bogz><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=Bogz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=842199\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P ⊃ (Q ∨ ∼P)\r<BR>\n" );
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document.write( "= ~P V (Q ∨ ∼P)    (equivalence to implication)\r<BR>\n" );
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document.write( "= ~P V (~P ∨ Q)     (commutativity)\r<BR>\n" );
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document.write( "= (~P V ~P) ∨ Q     (associativity)\r<BR>\n" );
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document.write( "= ~P V Q            (simplification)\r<BR>\n" );
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document.write( "= P ⊃ Q            (equivalence to implication) </SPAN>\n" );
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