Given set A {2,8,1}
set B {4,3,1}
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| = 3 · 3
|A × B| = 9
Show ordered pair grid:
| 4 | 3 | 1 | |
| 2 | (2, 4) | (2, 3) | (2, 1) |
| 8 | (8, 4) | (8, 3) | (8, 1) |
| 1 | (1, 4) | (1, 3) | (1, 1) |
Ordered pair setup:
(2,4)
(2,3)
(2,1)
Ordered pair setup:
(8,4)
(8,3)
(8,1)
Ordered pair setup:
(1,4)
(1,3)
(1,1)
Final Answer
{(2,4),(2,3),(2,1),(8,4),(8,3),(8,1),(1,4),(1,3),(1,1)}
What is the Answer?
{(2,4),(2,3),(2,1),(8,4),(8,3),(8,1),(1,4),(1,3),(1,1)}
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.
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)
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
