Equivalence relations and equivalence classes
A relation on a set A is called an equivalence relation if it is reflexive,
symmetric and transitive.
- … and … have the same age
- … is congruent to … modulo 2
Let R be an equivalence relation on a set A, and let a be an element of
A. The set of all elements of A that are related to a by R is called the
equivalence class for a and is denoted by [a].
If b?[a], b is called a representative of [a].
Example: Let A be the set of all integers, and R be the relation
“… is congruent to … modulo 2”. What is ?
--- The set of all even integers