What does this calculator compute?

This calculator compares finite sets written as comma-separated elements. Set A and set B are required, and set C can be added when you need a three-set union or intersection.

• A ∪ B contains every element that is in A, in B, or in both.
• A ∩ B contains only the elements that are common to A and B.
• A\B contains elements in A that are not in B.
• B\A contains elements in B that are not in A.
• A△B contains elements that are in exactly one of A or B.

What do union and intersection mean?

Union means everything that appears in at least one of the sets. Intersection means only what appears in all of the selected sets.

For example, if A = {1, 2, 3} and B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}, while A ∩ B = {3}. The element 3 appears in both sets, so it is the intersection.

How are difference and symmetric difference read?

Set difference is directional: A\B keeps what belongs to A but not to B. Symmetric difference keeps what belongs to exactly one of the two sets.

• A\B is the A-only part.
• B\A is the B-only part.
• A△B combines A\B and B\A.
• Elements common to both sets are not included in the symmetric difference.

This is useful when comparing two lists, groups, filters, tags, categories or result sets and you want to know what overlaps and what is unique to each side.

How to use the A, B and optional C inputs

Enter the elements of each set separated by commas. The calculator will de-duplicate repeated entries within the same set and then compare membership across the sets.

1. Enter set A, such as red, blue, green.
2. Enter set B, such as blue, yellow, green.
3. Turn on set C only if you need a three-set union or intersection.
4. Read the union, intersection, differences and symmetric difference from the result area.

Worked example: two sets

Let A = {apple, pear, cherry} and B = {cherry, banana, pear, fig}. The common elements are pear and cherry.

• A ∪ B = {apple, pear, cherry, banana, fig}
• A ∩ B = {pear, cherry}
• A\B = {apple}
• B\A = {banana, fig}
• A△B = {apple, banana, fig}

The example shows why symmetric difference is not the same as union: it removes the elements that are shared by both sets.

Worked example: three sets

Let A = {1, 2, 3}, B = {2, 3, 4} and C = {3, 4, 5}. The union contains everything that appears anywhere; the intersection keeps only what appears in all three.

• A ∪ B ∪ C = {1, 2, 3, 4, 5}
• A ∩ B ∩ C = {3}
• 2 is in A and B, but not in C, so it is not in the three-set intersection.
• 5 is in C only, so it belongs to the union but not the intersection.

What does the Venn diagram show?

In two-set mode, the Venn-style diagram is a conceptual guide that separates the A-only region, the shared region and the B-only region.

The drawing is not intended to scale circle areas proportionally to the number of elements. The result lists are the authoritative calculated output; the diagram helps you read the logic visually.

This is not an interval union calculator

The words union and intersection are also used for intervals, but this calculator is for finite element sets, not interval notation.

A simple test: if you are listing separate items, this set calculator is appropriate. If you are working with lower and upper bounds, use an interval calculator.

Common mistakes

Most mistakes come from counting repeated elements twice, reversing set difference, or mixing finite sets with interval notation.

• Do not count the same element twice in a union.
• Do not treat A\B and B\A as interchangeable.
• Do not include common elements in the symmetric difference.
• Do not treat an empty intersection as an error.
• Do not use this page for interval union or interval intersection.

Limitations and trust notes

The calculator performs exact membership operations on the elements you enter. It does not infer hidden categories, normalize spelling, or judge whether two differently written labels should be treated as the same item.

• Set A and set B cannot be empty.
• Set C is optional and only affects the three-set union and intersection outputs.
• Spelling matters: apple and Apple may be treated as different entries depending on input handling.
• The results are for finite listed sets, not infinite sets or interval objects.

Which related calculator should I use?

Choose the related calculator based on the type of set question you are asking.

• Use kuvvet-kumesi for a power set.
• Use alt-kume to check subset relationships.
• Use aralik-gosterimi for interval notation.
• Use sayi-dogrusunda-esitsizlik for inequalities on a number line.