document.write( "Question 1088368: the operation * defined on the set of real numbers by a*b=a+b+(ab)/2 for all a,b€R. is the operation * associative over the set R? \n" ); document.write( "

Algebra.Com's Answer #702649 by rothauserc(4718) $\"\"$ $\"About$

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let a,b,c be elements of R
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\n" ); document.write( "the associative property of Groups is
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\n" ); document.write( "(a * b) * c = a * (b * c)
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\n" ); document.write( "we will check this by direct computation
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\n" ); document.write( "(a * b) * c = (a+b+(ab)/2) * c =
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\n" ); document.write( "a+b+(ab)/2 + c + c(a+b+(ab)/2)/2 =
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\n" ); document.write( "1) a+b+(ab)/2 + c + ac/2 + bc/2 + abc/4
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\n" ); document.write( "a * (b * c) = a * (b + c + bc/2) =
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\n" ); document.write( "a +b+c+bc/2 + a(b+c+bc/2)/2 =
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\n" ); document.write( "2) a +b+c+bc/2 + ab/2 + ac/2 + abc/4
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\n" ); document.write( "expressions 1) and 2) are equal, so yes * is associative
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