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Explain in Detail :Cartesian Product Formula
The Cartesian product of two sets A and B, denoted by A × B, is the set of all ordered pairs (a, b) where a is an element of A and b is an element of B. It is written as:
A × B = {(a, b) | a ∈ A and b ∈ B}
For example, the Cartesian product of the sets A = {1, 2, 3} and B = {4, 5, 6} is A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}.
Interesting Facts About Cartesian Product
The Cartesian product of two sets is a set of all possible ordered pairs where the first element is from the first set and the second element is from the second set.
The Cartesian product of two sets is also called the cross product or Cartesian product of sets.
Cartesian Product and Ordered Pairs Examples
Given the sets:
A = {1, 2, 3}
B = {4, 5, 6}
The Cartesian product of A and B, written A × B, is the set of all possible ordered pairs (a, b) where a ∈ A and b ∈ B.
The ordered pairs are:
(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)
