Cartesian Product:

The Cartesian Product of two sets A and B is the set of all Ordered Pairs (a,b)  where the first element of order pairs “a” belongs to first set “A” and second element of ordered pairs “b” belongs or second set “B”.

Or a∈A and b∈B

Note: Cartesian product of set A and B is not equal to Cartesian product   of set B and A.

Denotation of Cartesian product:

Cartesian product of sets “A” and “B” is denoted by :

A×B

And Cartesian product of sets “B” and “A” is denoted by:

B×A

For example:

If set A={1,2} and set B={4,5}

Then,

A×B=[ {1,4} , {1,5} , {2,4} , {2,5} ]

And

B×A=[ {4,1} , {4,2} , {5,1} , {5,2} ]

Note: If “m” is the number of elements in set “A” and “n” is number of elements in set “B” then the numbers of elements of A×B and B×A is m×n

For example:

If set A have 2 elements and Set B have 3 elements the the number of elements that A×B and B×A have is 3×2=6.