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weird functions problem

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weird functions problem

by missrochelle » Mon Aug 30, 2010 3:04 pm
If the operation @ is defined for all integers a and b by a@b=a+b-ab,which of the following statements must be true for all integers a,b and c
I)a@b=b@a
II)a@0=a
III)(a@b)@c =a@(b@c)

Can someone explain how to factor III? Answer is all 3 are true.
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by Maciek » Mon Aug 30, 2010 3:36 pm
Hi Miss Rochelle!

I)a @ b = a + b - ab = b + a - ba = b @ a
II)a @ 0 = a + 0 - a*0 = a
III)(a @ b) @ c = (a + b - ab) + c - c(a + b - ab) = a + (b + c - bc) - a(b + c - bc) = a + (b @ c) - a(b @ c) = a@(b@c)

Hope it helps!
Best,
Maciek
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