# Category:Examples of Equivalence Relations

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This category contains examples of Equivalence Relation.

Let $\RR$ 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 12 subcategories, out of 12 total.

### D

### E

## Pages in category "Examples of Equivalence Relations"

The following 90 pages are in this category, out of 90 total.

### A

### C

- Ceiling defines Equivalence Relation
- Column Equivalence is Equivalence Relation
- Compatibility of Atlases is Equivalence Relation
- Conformality is Equivalence Relation on Set of Riemannian Metrics
- Congruence Modulo Integer is Equivalence Relation
- Congruence Modulo Real Number is Equivalence Relation
- Congruence Modulo Subgroup is Equivalence Relation
- Congruence of Triangles is Equivalence Relation
- Conjugacy is Equivalence Relation
- Connectedness Between Two Points is an Equivalence Relation
- Connectedness of Points is Equivalence Relation
- Cross-Relation on Natural Numbers is Equivalence Relation
- Cross-Relation on Real Numbers is Equivalence Relation

### D

### E

- Equality is Equivalence Relation
- Equality of Squares Modulo Integer is Equivalence Relation
- Equidecomposability is Equivalence Relation
- Equivalence Induced by Epimorphism is Congruence Relation
- Equivalence of Subobjects is Equivalence
- Equivalence Relation is Congruence for Constant Operation
- Equivalence Relation is Congruence for Left Operation
- Equivalence Relation is Congruence for Right Operation
- Equivalence Relation on Integers Modulo 5 induced by Squaring
- Equivalence Relation on Natural Numbers such that Quotient is Power of Two
- Equivalence Relation on Natural Numbers such that Quotient is Power of Two/Equivalence Class Contains 1 Odd Number
- 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/Equal Fourth Powers over Complex Numbers
- Equivalence Relation/Examples/Equal Sine of pi x over 6 on Integers
- 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
- Equivalence Relation/Examples/Points on Same Line

### H

### L

### P

- Parallelism is Equivalence Relation
- Path Homotopy is Equivalence Relation
- Path-Connectedness is Equivalence Relation
- Permutation Induces Equivalence Relation
- Permutation Induces Equivalence Relation/Corollary
- Preordering induces Equivalence Relation
- Proportion is Equivalence Relation
- Pseudometric Defines an Equivalence Relation

### R

- Relation Induced by Mapping is Equivalence Relation
- Relation Induced by Partition is Equivalence
- Relation Induced by Quotient Set is Equivalence
- Relation Isomorphism is Equivalence Relation
- Relation on Empty Set is Equivalence
- Restricted Dipper Relation is Equivalence Relation
- Right Congruence Modulo Subgroup is Equivalence Relation
- Row Equivalence is Equivalence Relation