CALCULATE WITH CONFIDENCE

Set Theory & Logic

Relation Operations & Closure Calculator

Find an inverse, compose two relations, or calculate a reflexive, symmetric, or transitive closure.

Set Theory & Logic

Enter values

Private calculation in your browser

Use the notation shown in each label and example. Inputs stay on this device and are never sent to a calculation service.

Result

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Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Quick guide

How to use this calculator

  1. Enter values using the notation shown beside each field.
  2. Choose a calculation mode when the tool offers more than one interpretation.
  3. Read the primary answer first, then inspect the supporting details.

Calculation method

Apply the stated definition

A closure is the smallest super-relation with the selected property.

The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.

Worked example

Worked example

The transitive closure of {(a,b),(b,c)} also contains (a,c).

A closure is the smallest super-relation with the selected property.

Supported inputs

Precision and limits

Finite, bounded input

Set and logic tools use finite inputs so every result can be checked completely. Each page states its practical size limit.

Notation

Set elements are comma-separated text labels. Logic operators and relation-pair notation are documented in the relevant input labels.