How to Find a Cartesian Product of 2 sets A and B using the unique ordered pair combinations from both sets. The Cartesian Product is A x B. To find the cardinality, |A x B|, we have |A| * |B|. Cartesian Product Calculator: https://www.mathcelebrity.com/cartprod.php

1. Cartesian Product
Definition: Given 2 sets A and B, the Cartesian
Product is the set of all unique ordered pairs
using one element from Set A and one element
from Set B.
The Cartesian Product is denoted as A x B
A x B = { (a, b) | a ∈ A and b ∈ B }
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2. Cartesian Product Formula
Take 2 sets, A and B.
The cardinality of a set equals the number of elements in the
set, denoted |A|.
The number of ordered pairs (cardinality) in the Cartesian
Product equal |A x B| = |A| * |B|
Each ordered pair is denote as {ai, bj} where…
● i is the ith element in Set A, j is the jth element in Set B 2

3. Cartesian Product Ordered Pair Grid
A = {a1, a2}, B = {b1, b2, b3}
|A x B| = |A| * |B|
|A x B| = 2 * 3 = 6
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b1 b2 b3
a1 (a1, b1) (a1, b2) (a1, b3)
a2 (a2, b1) (a2, b2) (a2, b3)

4. Cartesian Product Ordered Pair Final Answer
A x B = ((a1, b1), (a1, b2), (a1, b3), (a2, b1), (a2, b2), (a2, b3)}
A = {a1, a2}, B = {b1, b2, b3}
4
b1 b2 b3
a1 (a1, b1) (a1, b2) (a1, b3)
a2 (a2, b1) (a2, b2) (a2, b3)

5. Cartesian Product Example
A = {1, 3}, B = {2, 4, 6}
|A| = 2, |B| = 3 → |A x B| = 2 * 3 = 6
The Cartesian Product A x B contains 2 * 3 = 6 ordered pairs
(a1, b1), (a1, b2), (a1, b3) = (1, 2), (1, 4), (1, 6)
(a2, b1), (a2, b2), (a2, b3) = (3, 2), (3, 4), (3, 6)
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6. Cartesian Product Example Ordered Pair Grid
A = {1, 3}, B = {2, 4, 6}
(a1, b1), (a1, b2), (a1, b3) = (1, 2), (1, 4), (1, 6)
(a2, b1), (a2, b2), (a2, b3) = (3, 2), (3, 4), (3, 6)
6
b1 b2 b3
a1 (1, 2) (1, 4) (1, 6)
a2 (3, 2) (3, 4) (3, 6)

7. Cartesian Product Example Final Answer
A = {1, 3}, B = {2, 4, 6}
A x B = {(1, 2), (1, 4), (1, 6), (3, 2), (3, 4), (3, 6)}
7
b1 b2 b3
a1 (1, 2) (1, 4) (1, 6)
a2 (3, 2) (3, 4) (3, 6)