In the last chapter we introduced relations. We will now look at three useful properties of relations: relations might be reflexive, symmetric, or transitive. Those that are all three, like the familiar “equals” relation, are called equivalence relations. We introduce equivalence classes, with a focus on notation. Students should work the solved exercises, which include many examples and nonexamples of equivalence relations, as well as examples involving directed graphs that aim to help students picture these properties. In a section Tips on Reading we stress that reading mathematics is an active rather than passive activity; it’s important to check your proof with a pencil in hand and paper nearby.