# Ordered pairs and cartesian products | Sets in Mathematics

Here is discussed about Ordered pairs and Cartesian product in the set. Both are important in the perspective of the set in mathematics.

## Ordered pairs and cartesian products

### Ordered pairs

Cartesian product of two sets A, B is the set of all possible ordered pairs. Ordered pairs, in this case, will be denoted by A✕B.
• In Ordered pairs, there are two elements a and b where a is the first element and b is the second.

#### Ordered pair example

(a,b), (c,d), (e,f)

Ordered pair characteristics
• Ordered pairs are defined by (a,b).
• Two Ordered pairs (a, b) and (c,d) are equal one and only when a = c and b=d.
• (a, b) and (b, a) are not same Ordered pairs but {2, 3} and {3, 2} both are same sets.

### Cartesian products

Let, A, B are two given sets. Also, a∈A and b∈B. Then all Ordered pairs (a, b) will be called Cartesian product.

• Cartesian Product represented as A⨯B. Read as A cross B.
• In a short way, A⨯B = {(a, b) :a∈A , b∈B }

Here is  an example

Two sets are given A ={1,2,3} and B = {4,5}. Then the Cartesian product set will be -

A⨯B = {(1, 4), (1, 5), (2, 4), (2, 5), (3, 4), (3, 5)}

Here,

• Number of members of set A = 3
• Number of members of set B = 2
• Number of members of Cartesian product set = 6

#### Remember

If the number of members of set A and set B is m and n then the number of members of the Cartesian product set is mn.