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Let S={1, 2, 3, 4 ..., n} be a set. Suppose we define a new binary operator • that combines two elements of S to form an element of S (this element can be equal one of the two original elements.

 

Now suppose x•1=1•x=x. And x•(y•z)=(x•y)•(x•z).

 

Prove that x•(y•z)=(x•y)•z.

 Feb 18, 2020
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 Feb 21, 2020

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