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Operation is associative - [Iran Second Round 1984]

Source:

December 30, 2010
algebra proposedalgebra

Problem Statement

Define the operation ⨁\bigoplus on the set of real numbers such that x⨁y=x+y−xy∀x,y∈R.x \bigoplus y = x+y-xy \qquad \forall x,y \in \mathbb R. Prove that this operation is associative.
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