Understand the subject
What does a Hasse diagram simplify?
A Hasse diagram keeps only cover relations in a partial order, omitting self-links and arrows implied by longer paths.
Use it to read what is immediately above or below an element without visual clutter.
See the structure
What the rule checks
421
a covers b when b<a and no c satisfies b<c<aWorked interpretation
Read the result in context
For divisibility 1|2|4, the covers are 1–2 and 2–4.
Interpret with care
Important boundary
A Hasse diagram requires a valid partial order; not every relation can be drawn this way.
Use the Set Operations Calculator to explore small finite examples.
Quick guide
How to use this calculator
- Enter values using the notation shown beside each field.
- Choose a calculation mode when the tool offers more than one interpretation.
- 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 a≤b≤c, the covers are (a,b) and (b,c).
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.
