Understand the subject
What is a Cartesian product?
A Cartesian product makes every ordered pair by matching each first-set member with every second-set member.
Use it to list all possible two-part outcomes or finite input-output pairs.
See the structure
What the rule checks
(1,x)(1,y)(2,x)(2,y)
A×B={(a,b):a∈A,b∈B}; |A×B|=|A||B|Worked interpretation
Read the result in context
{1,2}×{x,y} has four ordered pairs.
Interpret with care
Important boundary
Order matters: (a,b) and (b,a) are different unless the entries happen to match.
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×B={(a,b): a∈A and b∈B}
The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.
Worked example
Worked example
{1,2}×{x,y} has four ordered pairs.
A×B={(a,b): a∈A and b∈B}
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.
