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.

Guest Feb 18, 2020