Cartesian product of two sets.





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.



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