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 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.
Between these ordered pairs, different types of relations can be defined.

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.

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