SOLUTION: The operation * is defined on the set of real numbers by a*b=a+b+ab/2. Is the operation associative

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Question 683768: The operation * is defined on the set of real numbers by a*b=a+b+ab/2. Is the operation associative
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
we check that (a*b)*c = a*(b*c)

(a*b)*c = (a+b+ab/2)*c =
a+b+ab/2 +c + ((a+b+ab/2)c)/2=



a*(b*c) = a*(b+c+bc/2) =
a+(b+c+bc/2)+(a((b+c+bc/2))/2


comparing...
(a+b+ab/2 +c + ((a+b+ab/2)c)/2) -
(a+(b+c+bc/2)+(a((b+c+bc/2))/2)
which is 0

the operation is associative

:)