Relation Properties Calculator
Verified Calculation Engine
The online Relation Properties 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 reflexive, symmetric, transitive, or antisymmetric.
Reflexive: (a, a) ∈ R for all a ∈ A
Symmetric: If (a, b) ∈ R then (b, a) ∈ R
Transitive: If (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R
Antisymmetric: If (a, b) ∈ R and (b, a) ∈ R then a = b
Properties of relations: reflexive, symmetric, transitive, antisymmetric
Inputs
Results
Worked Examples
Example 1: Check Properties
Set A = {1, 2, 3}, Relation R = {(1,1), (2,2), (3,3), (1,2), (2,1)}
- set: [ 1, 2, 3 ]
- relation: [ [ 1, 1 ], [ 2, 2 ], [ 3, 3 ], [ 1, 2 ], [ 2, 1 ] ]
- isReflexive: true
- isSymmetric: true
- isTransitive: false
- isAntisymmetric: false
Example 2: Equality Relation
Set A = {1, 2, 3}, Relation R = {(1,1), (2,2), (3,3)} (equality relation)
- set: [ 1, 2, 3 ]
- relation: [ [ 1, 1 ], [ 2, 2 ], [ 3, 3 ] ]
- isReflexive: true
- isSymmetric: true
- isTransitive: true
- isAntisymmetric: true
About this calculator
Overview
Relation Properties Calculator evaluates Relation Properties for the math / sets-relations-functions library. Primary input cue: Set [required]: Set on which relation is defined. Method anchor: Reflexive: (a, a) ∈ R for all a ∈ A Symmetric: If (a, b) ∈ R then (b, a) ∈ R Transitive: If (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R Antisymmetric: If (a, b) ∈.
When to use
Use Relation Properties Calculator when you already know the inputs and need relation properties without setting up a spreadsheet.
Inputs explained
- Set [required]: Set on which relation is defined
- Relation [required]: Relation as array of ordered pairs [[a1, b1], [a2, b2], ...]
Formula / method
Reflexive: (a, a) ∈ R for all a ∈ A Symmetric: If (a, b) ∈ R then (b, a) ∈ R Transitive: If (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R Antisymmetric: If (a, b) ∈ R and (b, a) ∈ R then a = b. Properties of relations: reflexive, symmetric, transitive, antisymmetric (calculator id: relation-properties-calculator).
Worked example
Worked values: set = [1, 2, 3], relation = [[1, 1], [2, 2], [3, 3], [1, 2], [2, 1]] → isReflexive = True, isSymmetric = True, isTransitive = False, isAntisymmetric = False
Interpreting results
Read the primary output as relation properties under the method on this page.
Assumptions
- Units (when shown) must be consistent across inputs for relation properties. [relation-properties-calculator]
- Empty required inputs are not silently replaced with zeros for relation properties.
- Real-number arithmetic is used unless relation properties explicitly needs integers.
Limitations
- This page does not provide a full textbook proof for every identity related to relation properties.
- Relation Properties Calculator cannot invent missing inputs; incomplete forms stop short of a forged relation properties value.
- Complex/branch cuts and undefined points are not always interactively annotated for relation properties.
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
Reflexive: (a, a) ∈ R for all a ∈ A Symmetric: If (a, b) ∈ R then (b, a) ∈ R Transitive: If (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R Antisymmetric: If (a, b) ∈ R and (b, a) ∈ R then a = b. Properties of relations: reflexive, symmetric, transitive, antisymmetric (calculator id: relation-properties-calculator).
Example Calculation
Worked values: set = [1, 2, 3], relation = [[1, 1], [2, 2], [3, 3], [1, 2], [2, 1]] → isReflexive = True, isSymmetric = True, isTransitive = False, isAntisymmetric = False
Frequently Asked Questions
What is Relation Properties Calculator?
- Relation Properties Calculator evaluates Relation Properties for the math / sets-relations-functions library. Primary input cue: Set [required]: Set on which relation is defined. Method anchor: Reflexive: (a, a) ∈ R for all a ∈ A Symmetric: If (a, b) ∈ R then (b, a) ∈ R Transitive: If (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R Antisymmetric: If (a, b) ∈.
How does Relation Properties Calculator work?
- Reflexive: (a, a) ∈ R for all a ∈ A Symmetric: If (a, b) ∈ R then (b, a) ∈ R Transitive: If (a, b) ∈ R and (b, c) ∈ R then (a, c) ∈ R Antisymmetric: If (a, b) ∈ R and (b, a) ∈ R then a = b. Properties of relations: reflexive, symmetric, transitive, antisymmetric (calculator id: relation-properties-calculator).
Why use this Math Numbers calculator?
- Use Relation Properties Calculator when you already know the inputs and need relation properties without setting up a spreadsheet.