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