Understand the subject
What is a set expression?
A set expression combines operations such as union, intersection, difference, and complement into one membership rule.
Use it to evaluate a finite expression or test whether two expressions agree under entered sets.
See the structure
What the rule checks
Worked interpretation
Read the result in context
Distributing A over B∪C yields the same members on both sides.
Interpret with care
Important boundary
An identity is checked relative to the supplied finite universe when complements occur.
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
Complement is relative to the stated universal set.
The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.
Worked example
Worked example
A∩(B∪C) can be checked against (A∩B)∪(A∩C).
Complement is relative to the stated universal set.
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.
