The mathematical idea behind Set Union
On this page, the displayed set union follows this definition rather than any similarly named measure.
Math calculator
Set Union Calculator
Combine the distinct elements appearing in either of two finite sets. Its set union sits beside the working formula for a quick arithmetic check.
Set Union inputs
Set up the calculation
Working through Set Union
Copy A, then append each B element not already present and compare the result with both inputs.
The union A∪B contains every element that belongs to A, B, or both, with duplicates represented once. Set Union can be compared with shared elements.
Set Union: a worked example
For A={red,blue,green} and B={blue,yellow}, the union is {red,blue,green,yellow}.
Where Set Union is useful
Union combines categories, survey responses, database keys, permissions, and finite collections without losing members unique to either source.
Boundary cases in Set Union
Order is only a display choice, and repeated input labels do not create extra set members.
Keep the element convention and input roles beside the source values; the browser cannot infer a silent mismatch in Set Union.
Connecting Set Union inputs and output
When reporting Set Union, retain Set A and Set B with enough working detail to distinguish the calculated value from a separately rounded presentation.
How Set Union changes
Adding an element already present changes nothing; adding a new element raises cardinality by one. Predict that movement before recalculating the set union; disagreement points to an input-role or sign issue.
Recording Set Union
In Set Union, the labels matter as much as the values. Check Set A against the source, then test whether Set B behaves as the formula predicts.
Intersection keeps only shared members instead of every member. Here the requested quantity is specifically set union.
Preserve the Set Union formula beside Set A and Set B; that small record makes a later independent calculation possible.
Checking the combined membership
Every original member must appear, while an element shared by A and B must appear only once.
Questions about Set Union
What does Set Union calculate?
The union A∪B contains every element that belongs to A, B, or both, with duplicates represented once.
When is Set Union useful?
Union combines categories, survey responses, database keys, permissions, and finite collections without losing members unique to either source.
What can make Set Union misleading?
Order is only a display choice, and repeated input labels do not create extra set members.
Checking Set Union independently
Copy A, then append each B element not already present and compare the result with both inputs.