# Category:Examples of Equivalence Relations

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This category contains examples of Equivalence Relation.

Let $\mathcal R$ be a relation on a set $S$.

Let $\RR$ be:

- $(1): \quad$ reflexive
- $(2): \quad$ symmetric
- $(3): \quad$ transitive

Then $\RR$ is an **equivalence relation** on $S$.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Examples of Equivalence Relations"

The following 26 pages are in this category, out of 26 total.

### E

- Equals is Equivalence Relation
- Equivalence Relation on Integers Modulo 5 induced by Squaring
- Equivalence Relation on Natural Numbers such that Quotient is Power of Two
- Equivalence Relation on Power Set induced by Intersection with Subset
- Equivalence Relation on Square Matrices induced by Positive Integer Powers
- Equivalence Relation/Examples
- Equivalence Relation/Examples/Books with Same Number of Pages
- Equivalence Relation/Examples/Even Sum
- Equivalence Relation/Examples/Months that Start on the Same Day of the Week
- Equivalence Relation/Examples/Non-Equivalence
- Equivalence Relation/Examples/Non-Equivalence/Divisor Relation
- Equivalence Relation/Examples/Non-Equivalence/Greater Than
- Equivalence Relation/Examples/Non-Equivalence/Is the Mother Of
- Equivalence Relation/Examples/Non-Equivalence/Is the Sister Of
- Equivalence Relation/Examples/Non-Equivalence/People of Different Age
- Equivalence Relation/Examples/Non-Equivalence/People with Common Ancestor
- Equivalence Relation/Examples/Non-Equivalence/Sum is Integer
- Equivalence Relation/Examples/Non-Equivalence/Sum of Integers is Divisible by 3
- Equivalence Relation/Examples/People of Same Age
- Equivalence Relation/Examples/People with Same First Name
- Equivalence Relation/Examples/People with Same Parents