math1081-assignment/q2/e.md

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.