document.write( "Question 1161344: Show by contraposition that if n is an integer n³+5 is odd then n is even \n" ); document.write( "

Algebra.Com's Answer #784856 by math_helper(2461) $\"\"$ $\"About$

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document.write( "Let P be  is odd
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document.write( "and Q be  is even\r
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document.write( "The problem asks to show P --> Q by showing ~Q --> ~P   (notice these are logically equivalent statements).  \r
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document.write( "\"If it rains then the garden will be watered.\"  is logically equivalent to
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document.write( "\"If the garden is not watered then it did not rain.\"\r
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document.write( "~Q means n is not even (i.e. n is odd)\r
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document.write( "1. Assume n is odd
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document.write( "2.  is odd (odd x odd is odd, so odd x odd x odd is also odd)
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document.write( "3.  is even  (odd + odd is even)
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document.write( "4.  ~Q --> ~P
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document.write( "5.  P --> Q       \r
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