Set Calculator
Perform set operations: union, intersection, difference, symmetric difference, cartesian product and set relations.
About this calculator
Operate on two sets entered as comma-separated values. The tool returns union, intersection, difference, and symmetric difference, plus set membership checks.
Set operations
- Union (A ∪ B) — everything in A or B.
- Intersection (A ∩ B) — only items in both A and B.
- Difference (A − B) — items in A but not in B.
- Symmetric difference — items in either set but not both.
How to enter sets
Type values separated by commas, e.g. 1, 2, 3. Duplicates are removed automatically because a set holds each element at most once.
Where this is used
Set logic underpins database queries, probability, logic design, and data de-duplication.
How to use Set Calculator
- 1Enter a set of A and B elements, separated by commas.
- 2Select the operation: combined, intersecting, differential or symmetrical.
- 3View the results of the collection to list the members after they are heavy.
Collapse Operations
A-B, a-B, a-B, a-B, symmetry (A-B) ∪ (B-A)The aggregation is a collection of different elements; the aggregation combines or compares the collections without double counting.
All reservations are kept together, only the same items are retained at the intersection, and the different reservations belong to one but not the other.
A-B is "in A but not in B" and B-A is "in B but not in A", which is not the same. Using the example of the above table, A -B = {1, 2}, while B -A = {4, 5}. Adjudication techniques: First look at the assembly in front of the minus sign and remove from it the elements in the back.
The principle of rebuke is the most important practical formula for aggregate calculations: |A =B= = |B+ − B−. Direct additions count the intersections twice, so they are reduced once. In the previous example, =A = 3, =B = 3, =A ∩ B = 1, so |A ∪B = 3 + 3 = 1 = 5, which corresponds to the actual {1, 2, 3, 4, 5}. This rationale, which can be extended to three or more clusters, is the basic tool for probabilistic and counting questions.
| Operations | Symbol | Meaning | Example (A = {1, 2, 3}, B = {3, 4, 5}) |
|---|---|---|---|
| Group | A ∪ B | All elements belonging to A or B | {1, 2, 3, 4, 5} |
| Intersection | A ∩ B | Elements of both A and B | {3} |
| Gap | A − B | Elements belonging to A but not B | {1, 2} |
| Complement | A′ | All elements that do not belong to A | Depends on the full set definition |
| Symmetry difference | A △ B | It's just one of the elements. | {1, 2, 4, 5} |
Basic calculations of the collection
Frequently asked questions
Why is there no repetition?
Each element will appear at most once by definition and will be merged.
What's a symmetry gap?
It happens to be an element of one of the two pools, excluding shared members.
Are you in order?
No, {1,2, 3} equals {3,2,}; only concerned about membership.
Can the elements in the collection repeat?
No, it's the core difference between a collection and a `list/multiset'. Each element of the assembly can only appear once, and {1, 1, 2} and {1, 2} are the same. Also ** There is no order**, {1, 2, 3} and {3, 2,} exactly the same. If the business needs to retain the number or order of repetitions, multisets (multisets) or lists/arrays should be used. The DISTINCT operation in the database is essentially about weighting the results as a grouping process.
How does a pool of operations work in programming?
Most languages have built-in collection types: Python uses set (support for & cross-section, t-coding, − differential, ^ symmetry), JavaScript has Set (need to run or expand) and SQL uses UNION/INTERSECT/EXCEPT. The bottom of the collection is usually a Hashi table, so the average complexity of finding and inserting is O (1), weighting and member judgement are highly efficient. When dealing with tasks such as "discovering the difference between the two lists", the collection is much faster than the embedded loop.