Equivalence Relations
A binary relation B on S is an equivalence relation provided that it is reflexive (on S), symmetric, and transitive.
R10 = { (a, a), (a, b), (b, a), (b, b), (c, c) } is an equivalence relation.
R9 = { (a, a), (a, b), (b, b), (b, c), (c, c)} is not an equivalence relation; although it is reflexive on {a, b, c}, it is not symmetric, and it is not transitive.
When we study the UNION-FIND abstract data type, we will use equivalence relations.