SOLUTION: 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?

SOLUTION: the operation * defined on the set of real numbers by ab=a+b+(ab)/2 for all a,b�R. is the operation associative over the set R?

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?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
let a,b,c be elements of R
:
the associative property of Groups is
:
(a * b) * c = a * (b * c)
:
we will check this by direct computation
:
(a * b) * c = (a+b+(ab)/2) * c =
:
a+b+(ab)/2 + c + c(a+b+(ab)/2)/2 =
:
1) a+b+(ab)/2 + c + ac/2 + bc/2 + abc/4
:
a * (b * c) = a * (b + c + bc/2) =
:
a +b+c+bc/2 + a(b+c+bc/2)/2 =
:
2) a +b+c+bc/2 + ab/2 + ac/2 + abc/4
:
expressions 1) and 2) are equal, so yes * is associative
:

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