document.write( "Question 1096698: Prove or disprove algebraically: The sum of an even number and an odd number is odd. \n" ); document.write( "
Algebra.Com's Answer #711100 by jim_thompson5910(35256)\"\" \"About 
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\n" ); document.write( "k = any integer
\n" ); document.write( "2*k = any even integer
\n" ); document.write( "2*k+1 = any odd integer\r
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\n" ); document.write( "\n" ); document.write( "Add up the even number (2*k) and the odd number (2*k+1) to get the following:\r
\n" ); document.write( "\n" ); document.write( "( 2*k ) + ( 2*k+1 )
\n" ); document.write( "2*k + 2*k+1
\n" ); document.write( "(2*k + 2*k)+1
\n" ); document.write( "(2+2)*k+1
\n" ); document.write( "4*k+1 \r
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\n" ); document.write( "\n" ); document.write( "Then we can rewrite that last expression like so:
\n" ); document.write( "4*k+1
\n" ); document.write( "(2*2)*k+1
\n" ); document.write( "2*(2*k)+1 \r
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\n" ); document.write( "\n" ); document.write( "If we let m = 2*k, then we have the expression 2*m+1 which is an odd number (since m is also an integer)\r
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\n" ); document.write( "\n" ); document.write( "Therefore the initial claim The sum of an even number and an odd number is odd is always true. This concludes the proof.
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