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Hello Operator (Posted on 2003-10-17) Difficulty: 4 of 5
Consider a binary operation # that is closed under the set of integers (if a and b are integers, then a#b is an integer).

Assume that, for all integers a and b, it is true that (a#b)#a=b.

Prove that a#(b#a)=b.

See The Solution Submitted by DJ    
Rating: 4.2727 (11 votes)

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Solution another way to describe it | Comment 3 of 19 |
Without using a different notation, we can substitute (a#b) for the old a and a for the old b:

((a#b)#a)#(a#b) = a

Now, replacing the (a#b)#a within this expression with b, as we are still entitled to do, we get

b#(a#b)=a

Now, renaming b as a and a as b:

a#(b#a)=b
  Posted by Charlie on 2003-10-17 15:07:18
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