document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248852>Question 248852</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Decide whether the argument is an example of inductive or deductive reasoning.<BR>\n" );
document.write( "37 + 19 = 56, 7 + 29 = 36, 41 + 7 = 48. The sum of two prime numbers is even. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181370 by </B><A HREF=/tutors/aboutme.mpl?userid=chosenpoint><B>chosenpoint(26)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=chosenpoint><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=chosenpoint><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=181370\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ******EDITED TO ADD THE FOLLOWING:******<br>\r<BR>\n" );
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document.write( "******As tutor Alan3354 pointed out, 2 is a prime number, so the following deductive reasoning works for all prime numbers except 2.  It was not a complete proof, just an idea of the difference between inductive and deductive reasoning.  I will edit the statement/answer below.******<br>  \r<BR>\n" );
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document.write( "To quickly follow up on this,<br>\r<BR>\n" );
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document.write( "We can use deductive reasoning in the following manner (this is NOT a complete proof, just an example of deductive reasoning).<br>  \r<BR>\n" );
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document.write( "As the other tutor stanbon said in the original answer, inductive reasoning is based on examples, deductive reasoning is based on the general case!<br>\r<BR>\n" );
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document.write( "Let x be any prime number EXCEPT 2 (which by definition will be odd, since it can not have 2 as a divisor).<br>\r<BR>\n" );
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document.write( "Let y be any prime number EXCEPT 2 (which can equal x, which will also be odd by definition).<br>\r<BR>\n" );
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document.write( "Since the sum of 2 odd numbers will always be even (using properties of integers), the sum of 2 prime numbers will also then be even.<br>\r<BR>\n" );
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document.write( "x + y = an even number<br>\r<BR>\n" );
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document.write( "The sum of any 2 prime numbers will always be even, unless ONLY ONE of those prime numbers is 2.  Of course if both of those prime numbers are 2, then you again have a sum that is an even number.  :)<br> </SPAN>\n" );
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