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part e

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### Part E
> Is $\star$ an equivalence relation, a partial order, both, or neither?
A relation is an equivalence relation if it is reflexive, symmetric and transitive. It was shown in parts A, B, and D that $\star$ meets these criteria.
A relation is a partial order if it is reflexive, anti-symmetric, and transitive. It was shown in parts A, B, and C that $\star$ meets these criteria.
Therefore, $\star$ is both an equivalence relation and a partial order.