Understand the subject
What are relation properties?
A finite relation is a set of ordered pairs that can be tested for patterns such as reflexivity, symmetry, antisymmetry, and transitivity.
Use it to classify a relation before deciding whether it can be an order or equivalence relation.
See the structure
What the rule checks
a → b → cthereforea → ctransitive: aRb and bRc imply aRc
Worked interpretation
Read the result in context
≤ on a finite ordered set is reflexive, antisymmetric, and transitive.
Interpret with care
Important boundary
A relation can be symmetric and antisymmetric only in limited cases; properties must be checked pair by pair.
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
Check reflexivity, symmetry, antisymmetry, asymmetry, and transitivity.
The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.
Worked example
Worked example
The ≤ relation on a finite ordered set is a partial order.
Check reflexivity, symmetry, antisymmetry, asymmetry, and transitivity.
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.
