Given two number sets A and B, this determines the following:

* Union of A and B, denoted A U B

* Intersection of A and B, denoted A ∩ B

* Elements in A not in B, denoted A - B

* Elements in B not in A, denoted B - A

* Symmetric Difference A Δ B

* The Concatenation A · B

* The Cartesian Product A x B

* Cardinality of A = |A|

* Cardinality of B = |B|

* Jaccard Index J(A,B)

* Jaccard Distance J_{σ}(A,B)

* Dice‘s Coefficient

* If A is a subset of B

* If B is a subset of A

This calculator has 2 inputs.

* Union of A and B, denoted A U B

* Intersection of A and B, denoted A ∩ B

* Elements in A not in B, denoted A - B

* Elements in B not in A, denoted B - A

* Symmetric Difference A Δ B

* The Concatenation A · B

* The Cartesian Product A x B

* Cardinality of A = |A|

* Cardinality of B = |B|

* Jaccard Index J(A,B)

* Jaccard Distance J

* Dice‘s Coefficient

* If A is a subset of B

* If B is a subset of A

This calculator has 2 inputs.

- A Δ B = (A - B) U (B - A)
- A
^{C}= U - A - A ∩ B = A + B - A U B
- J(A,B) = |A ∩ B|/|A U B|
- J
_{σ}(A,B) = 1 - J(A,B)

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- cardinality
- a measure of the number of elements of the set
- coefficient
- a numerical or constant quantity placed before and multiplying the variable in an algebraic expression
- difference
- the result of one of the important mathematical operations, which is obtained by subtracting two numbers
- element
- an element (or member) of a set is any one of the distinct objects that belong to that set. In chemistry, any substance that cannot be decomposed into simpler substances by ordinary chemical processes.
- index
- an indicator, sign, or measure of something
- intersection
- the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A.

A ∩ B - product
- The answer when two or more values are multiplied together
- set
- a collection of different things; a set contains elements or members, which can be mathematical objects of any kind
- set notation
- Ways of writing sets and their elements and properties
- subset
- A is a subset of B if all elements of the set A are elements of the set B
- union
- Combine the elements of two or more sets