Equivalence Relation Calculator
Verified Calculation Engine
The online Equivalence Relation Calculator helps you calculate instantly and solve problems related to Sets Relations Functions. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Checks if a relation is an equivalence relation and finds equivalence classes.
R is equivalence relation if:
1. Reflexive: (a, a) ∈ R for all a
2. Symmetric: If (a, b) ∈ R then (b, a) ∈ R
3. Transitive: If (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R
Equivalence class [a] = {b | (a, b) ∈ R}
Equivalence relation must be reflexive, symmetric, and transitive
Inputs
Results
Worked Examples
Example 1: Equivalence Relation
Set A = {1, 2, 3, 4}, R = {(1,1), (2,2), (3,3), (4,4), (1,2), (2,1), (3,4), (4,3)}
- set: [ 1, 2, 3, 4 ]
- relation: [ [ 1, 1 ], [ 2, 2 ], [ 3, 3 ], [ 4, 4 ], [ 1, 2 ], [ 2, 1 ], [ 3, 4 ], [ 4, 3 ] ]
- isEquivalence: true
- equivalenceClasses: [1,2], [3,4]
- partition: [1,2], [3,4]
Example 2: Modulo Equivalence
Set A = {0, 1, 2, 3, 4}, R = {(a,b) | a ≡ b (mod 3)}
- set: [ 0, 1, 2, 3, 4 ]
- relation: [ [ 0, 0 ], [ 0, 3 ], [ 3, 0 ], [ 3, 3 ], [ 1, 1 ], [ 1, 4 ], [ 4, 1 ], [ 4, 4 ], [ 2, 2 ] ]
- isEquivalence: true
- equivalenceClasses: [0,3], [1,4], [2]
- partition: [0,3], [1,4], [2]
About this calculator
Overview
Equivalence Relation Calculator evaluates Equivalence Relation for the math / sets-relations-functions library. Primary input cue: Set [required]: Set on which relation is defined. Method anchor: R is equivalence relation if: 1. Reflexive: (a, a) ∈ R for all a 2. Symmetric: If (a, b) ∈ R then (b, a) ∈ R 3. Transitive: If (a, b) ∈ R and (b, c) ∈ R then (a.
When to use
Appropriate when equivalence relation is the target quantity and the form fields match your known data.
Inputs explained
- Set [required]: Set on which relation is defined
- Relation [required]: Relation as array of ordered pairs
Formula / method
R is equivalence relation if: 1. Reflexive: (a, a) ∈ R for all a 2. Symmetric: If (a, b) ∈ R then (b, a) ∈ R 3. Transitive: If (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R Equivalence class [a] = {b | (a, b) ∈ R}. Equivalence relation must be reflexive, symmetric, and transitive (calculator id: equivalence-relation-calculator).
Worked example
Worked values: set = [1, 2, 3, 4], relation = [[1, 1], [2, 2], [3, 3], [4, 4], [1, 2], [2, 1], [3, 4], [4, 3]] → isEquivalence = True, equivalenceClasses = [[1, 2], [3, 4]], partition = [[1, 2], [3, 4]]
Interpreting results
If equivalence relation looks implausible, re-check units and which field is optional vs required.
Assumptions
- Empty required inputs are not silently replaced with zeros for equivalence relation. [equivalence-relation-calculator]
- Equivalence Relation is computed only from the fields you enter on this calculator.
- Real-number arithmetic is used unless equivalence relation explicitly needs integers.
Limitations
- If multiple conventions exist for equivalence relation, this calculator uses the convention implemented in its engine path.
- This page does not provide a full textbook proof for every identity related to equivalence relation.
- Complex/branch cuts and undefined points are not always interactively annotated for equivalence relation.
Important note
Educational mathematics tool. Check edge cases and domain restrictions when results look unexpected.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
R is equivalence relation if: 1. Reflexive: (a, a) ∈ R for all a 2. Symmetric: If (a, b) ∈ R then (b, a) ∈ R 3. Transitive: If (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R Equivalence class [a] = {b | (a, b) ∈ R}. Equivalence relation must be reflexive, symmetric, and transitive (calculator id: equivalence-relation-calculator).
Example Calculation
Worked values: set = [1, 2, 3, 4], relation = [[1, 1], [2, 2], [3, 3], [4, 4], [1, 2], [2, 1], [3, 4], [4, 3]] → isEquivalence = True, equivalenceClasses = [[1, 2], [3, 4]], partition = [[1, 2], [3, 4]]
Frequently Asked Questions
What is Equivalence Relation Calculator?
- Equivalence Relation Calculator evaluates Equivalence Relation for the math / sets-relations-functions library. Primary input cue: Set [required]: Set on which relation is defined. Method anchor: R is equivalence relation if: 1. Reflexive: (a, a) ∈ R for all a 2. Symmetric: If (a, b) ∈ R then (b, a) ∈ R 3. Transitive: If (a, b) ∈ R and (b, c) ∈ R then (a.
How does Equivalence Relation Calculator work?
- R is equivalence relation if: 1. Reflexive: (a, a) ∈ R for all a 2. Symmetric: If (a, b) ∈ R then (b, a) ∈ R 3. Transitive: If (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R Equivalence class [a] = {b | (a, b) ∈ R}. Equivalence relation must be reflexive, symmetric, and transitive (calculator id: equivalence-relation-calculator).
Why use this Math Numbers calculator?
- Appropriate when equivalence relation is the target quantity and the form fields match your known data.