Equivalence relation

Let be a set. A binary relation on is said to be an equivalence relation if satisfies the following three properties:

1. For every element , . (Reflexive property)
2. If such that , then we also have . (Symmetric property)
3. If such that and , then we also have . (Transitive property)

Some common examples of equivalence relations:

• The relation equality, on the set of complex numbers.
• The relation (congruence), on the set of geometric figures in the plane.
• The relation (similarity), on the set of geometric figures in the plane.
• For a given positive integer , the relation , on the set of integers. (Congruence modulo n)

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