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## Main Question or Discussion Point

I am not exactly clear on what an equivalence relation. If A is a set, then a relation on A is a subset R. The relation R is an equivalence relation on A if it satisfies the reflexive property, symmetric property, and transitive property. What types of relations are we talking about. And when could these relations ever not have these 3 properties. And what are equivalence classes? I need some simple examples to demonstrate this since none are really provided in this textbook.