Relation Composition Calculator
Verified Calculation Engine
The online Relation Composition 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.
Finds the composition of two relations R and S: S ∘ R = {(a, c) | (a, b) ∈ R and (b, c) ∈ S}.
S ∘ R = {(a, c) | ∃ b such that (a, b) ∈ R and (b, c) ∈ S}
Composition S ∘ R connects elements through intermediate elements
Inputs
Results
Worked Examples
Example 1: Basic Composition
R = {(1, 2), (2, 3)}, S = {(2, 4), (3, 5)}
- relationR: [ [ 1, 2 ], [ 2, 3 ] ]
- relationS: [ [ 2, 4 ], [ 3, 5 ] ]
- composition: [1,4], [2,5]
- reverseComposition:
Example 2: Complex Composition
R = {(1, 2), (1, 3), (2, 3)}, S = {(2, 4), (3, 4), (3, 5)}
- relationR: [ [ 1, 2 ], [ 1, 3 ], [ 2, 3 ] ]
- relationS: [ [ 2, 4 ], [ 3, 4 ], [ 3, 5 ] ]
- composition: [1,4], [1,4], [1,5], [2,4], [2,5]
- reverseComposition:
About this calculator
Overview
Relation Composition Calculator evaluates Relation Composition for the math / sets-relations-functions library. Primary input cue: Relation R [required]: First relation as array of ordered pairs. Method anchor: S ∘ R = {(a, c) | ∃ b such that (a, b) ∈ R and (b, c) ∈ S}. Composition S ∘ R connects elements through intermediate elements.
When to use
Use this page when you need relation composition from known inputs and want a transparent arithmetic or symbolic check.
Inputs explained
- Relation R [required]: First relation as array of ordered pairs
- Relation S [required]: Second relation as array of ordered pairs
Formula / method
S ∘ R = {(a, c) | ∃ b such that (a, b) ∈ R and (b, c) ∈ S}. Composition S ∘ R connects elements through intermediate elements (calculator id: relation-composition-calculator).
Worked example
Worked values: relationR = [[1, 2], [2, 3]], relationS = [[2, 4], [3, 5]] → composition = [[1, 4], [2, 5]], reverseComposition = []
Interpreting results
Cross-check with a simple numeric example before relying on extreme inputs for relation composition.
Assumptions
- Empty required inputs are not silently replaced with zeros for relation composition. [relation-composition-calculator]
- Relation Composition is computed only from the fields you enter on this calculator.
- Real-number arithmetic is used unless relation composition explicitly needs integers.
Limitations
- If multiple conventions exist for relation composition, this calculator uses the convention implemented in its engine path.
- This page does not provide a full textbook proof for every identity related to relation composition.
- Complex/branch cuts and undefined points are not always interactively annotated for relation composition.
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
S ∘ R = {(a, c) | ∃ b such that (a, b) ∈ R and (b, c) ∈ S}. Composition S ∘ R connects elements through intermediate elements (calculator id: relation-composition-calculator).
Example Calculation
Worked values: relationR = [[1, 2], [2, 3]], relationS = [[2, 4], [3, 5]] → composition = [[1, 4], [2, 5]], reverseComposition = []
Frequently Asked Questions
What is Relation Composition Calculator?
- Relation Composition Calculator evaluates Relation Composition for the math / sets-relations-functions library. Primary input cue: Relation R [required]: First relation as array of ordered pairs. Method anchor: S ∘ R = {(a, c) | ∃ b such that (a, b) ∈ R and (b, c) ∈ S}. Composition S ∘ R connects elements through intermediate elements.
How does Relation Composition Calculator work?
- S ∘ R = {(a, c) | ∃ b such that (a, b) ∈ R and (b, c) ∈ S}. Composition S ∘ R connects elements through intermediate elements (calculator id: relation-composition-calculator).
Why use this Math Numbers calculator?
- Use this page when you need relation composition from known inputs and want a transparent arithmetic or symbolic check.