Set Operations Calculator
Set operations compare two collections of labels and show the combined values, shared values, and values found in only one collection. Repeated entries are removed before the results are calculated.
How to use this calculator
- Enter comma- or semicolon-separated values in each set. The calculator trims spaces and removes exact duplicate labels.
- Check the labels and units before applying the result to a real task.
- Change one input at a time when comparing scenarios.
Formula and method
A ∪ B = values in either set; A ∩ B = values in both; A B = values in A but not B
- A ∪ B = values in either set; A ∩ B = values in both; A B = values in A but not B
- Items are compared as text labels rather than coerced to numbers. For example, “01” and “1” are different items.
Worked examples
Worked example
Set A is {1, 2, 3}; set B is {2, 3, 4}.
The union is {1, 2, 3, 4}, the intersection is {2, 3}, and A minus B is {1}.
The union is {1, 2, 3, 4}, the intersection is {2, 3}, and A minus B is {1}.
Understanding the result
Set operations compare two collections of labels and show the combined values, shared values, and values found in only one collection. Repeated entries are removed before the results are calculated.
Items are compared as text labels rather than coerced to numbers. For example, “01” and “1” are different items.
Important notes
Items are compared as text labels rather than coerced to numbers. For example, “01” and “1” are different items.
Displayed values are rounded for readability; retain appropriate precision when continuing a calculation.
Frequently asked questions
Does order matter for a set?
Mathematically a set is unordered. The displayed values are sorted for readability, but that display order does not change the membership of a set.
How is the intersection different from the union?
The intersection keeps only values present in both sets. The union includes every distinct value appearing in either set.
Are duplicate inputs counted more than once?
No. Exact duplicate labels are removed before union, intersection and difference results are shown.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.