Calculate the Cartesian Product of {1,2,3,4,5} and {6,7,8,9,10}

Enter Sets below:

<-- Set A
<-- Set B
  

Given set A {1,2,3,4,5}

set B {6,7,8,9,10}

Calculate the Cartesian Product A × B

Cartesian Product Definition:

A × B
Set of all possible:
ordered pairs (a, b)

Calculate the cardinality of A × B

Number of set elements
For set A, we have |A|
For set B, we have |B|

Therefore, |A × B| = |A| · |B|

|A × B| = 5 · 5

|A × B| = 25

Show ordered pair grid:

 678910
1(1, 6)(1, 7)(1, 8)(1, 9)(1, 10)
2(2, 6)(2, 7)(2, 8)(2, 9)(2, 10)
3(3, 6)(3, 7)(3, 8)(3, 9)(3, 10)
4(4, 6)(4, 7)(4, 8)(4, 9)(4, 10)
5(5, 6)(5, 7)(5, 8)(5, 9)(5, 10)

Ordered pair setup:

(1,6)

(1,7)

(1,8)

(1,9)

(1,10)

Ordered pair setup:

(2,6)

(2,7)

(2,8)

(2,9)

(2,10)

Ordered pair setup:

(3,6)

(3,7)

(3,8)

(3,9)

(3,10)

Ordered pair setup:

(4,6)

(4,7)

(4,8)

(4,9)

(4,10)

Ordered pair setup:

(5,6)

(5,7)

(5,8)

(5,9)

(5,10)

Cartesian Product A × B:

{(1,6),(1,7),(1,8),(1,9),(1,10),(2,6),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10)}





What is the Answer?
{(1,6),(1,7),(1,8),(1,9),(1,10),(2,6),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10)}
How does the Cartesian Product Calculator work?
Free Cartesian Product Calculator - Given a Set A and Set B, this calculates the Cartesian Product A × B
This calculator has 2 inputs.

What 1 formula is used for the Cartesian Product Calculator?

The cartesian product, A x B is the set of all possible ordered pairs (a, b)

For more math formulas, check out our Formula Dossier

What 7 concepts are covered in the Cartesian Product Calculator?

cardinality
a measure of the number of elements of the set
cartesian
a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length
cartesian product
the product of two sets: the product of set X and set Y is the set that contains all ordered pairs ( x, y ) for which x belongs to X and y belongs to Y
A x B
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.
ordered pair
A pair of numbers signifying the location of a point
(x, y)
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
Cartesian Product Calculator Video

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