CALCULATE WITH CONFIDENCE

Set Theory & Logic

Partial Order & Hasse Diagram Calculator

Validate a finite partial order and extract its Hasse cover relations.

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.

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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

Remove reflexive and transitively implied edges from the order relation.

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

Worked example

Worked example

For 1|2|4, the covers are (1,2) and (2,4).

Remove reflexive and transitively implied edges from the order relation.

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.