Exercise 6, § 1

Let $\tau$ be a law of composition on a set E; let A be the subset of E consisting of the elements $x$ such that $x \tau (y \tau z) = (x \tau y) \tau z$ for all $y \in E, z \in E$; show that A is a stable subset of E and that the law induced on A by $\tau$ is associative.