document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196105>Question 1196105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Without tables prove thet [(A→B)&(B→C)]→ (A→C)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #828829 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3835)</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=828829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Imagine 3 dominoes labeled A,B,C\r<BR>\n" );
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document.write( "The notation A→B can be thought of as domino A falling to knock down domino B<BR>\n" );
document.write( "I.e. \"A knocks down B\"<BR>\n" );
document.write( "or \"A leads to B\"\r<BR>\n" );
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document.write( "Then B→C means \"B knocks down C\"\r<BR>\n" );
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document.write( "The two events (A→B)&(B→C) chain together to mean: \"A knocks down B\" and \"B knocks down C\"<BR>\n" );
document.write( "Rephrased: \"A leads to B leads to C\"\r<BR>\n" );
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document.write( "We can then cut out the middleman and conclude that knocking down A ultimately leads to C falling, which gives us A→C\r<BR>\n" );
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document.write( "This process can be extended to more than 3 terms.\r<BR>\n" );
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document.write( "For more information, check out the transitive property. <BR>\n" );
document.write( "A similar related idea is the term \"syllogism\" found in logic class. More specifically its often called a \"hypothetical syllogism\"\r<BR>\n" );
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document.write( "--------------------------------------------------------\r<BR>\n" );
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document.write( "A real world example:<BR>\n" );
document.write( "A = it rains<BR>\n" );
document.write( "B = the roads get wet<BR>\n" );
document.write( "C = there's a higher chance of an accident\r<BR>\n" );
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document.write( "Premise1: (A→B) = If it rains, then the roads get wet<BR>\n" );
document.write( "Premise2: (B→C) = If the roads get wet, then there's a higher chance of an accident<BR>\n" );
document.write( "Conclusion: (A→C) = If it rains, then there's a higher chance of an accident<BR>\n" );
document.write( "Event A causes event B which in turn leads to event C.<BR>\n" );
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