Understand the subject
What is a relation closure?
A closure adds only the ordered pairs needed to give a relation a chosen property.
Use it to make reflexive, symmetric, or transitive implications explicit.
See the structure
What the rule checks
a → b → cthereforea → ctransitive closure adds aRc when aRb and bRc
Worked interpretation
Read the result in context
From (a,b) and (b,c), transitive closure also needs (a,c).
Interpret with care
Important boundary
A closure preserves existing pairs; it is not an arbitrary redesigned relation.
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
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.
