# Cartesian product of sets

**Cartesian product of two sets :** cartesian product of two sets is a collection of all those ordered pair of A and set B whose first co-ordinate is an element of set A and second element is an element of set B. means each pair contain each sets one elements.

Example : if set A={1, 2, 3} and set B={5, 6} then cartesian product of set A and B is A*B={1, 2, 3} * {5, 6} = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6)} and
B*A={5, 6} * {1, 2, 3} = {(5, 1), (5, 2), (5, 3), (6, 1), (6, 2), (6, 3)}
**Cartesian product of more than two sets :** Cartesian product of more than two sets contain ordered pair of given sets whose first element is an element of first set, second element is an element of second set, third element is an element of third set and goes on.

example : if set A{1, 2} , set B={3, 4} and set C={5, 6} then Cartesian product of set A, set B and set C is A*B*C=A*[B*C]

={1, 2}*[{3, 4}*{5, 6}]

=
{1, 2} * {(3, 5), (3, 6), (4, 5), (4, 6)}

= {(1, 3, 5), (1, 3, 6), (1, 4, 5), (1, 4, 6), (2, 3, 5), (2, 3, 6), (2, 4, 5), (2,4, 6)}
**Ordered pair :** ordered pair of elements or objects is a pair of elements or objects those written in particular order.

## Number of elements in cartesian product

**Number of elements of a set :**number of element, object, member of any finite set A is denoted by n(A). if any set A={1, 2, 3} then n(A)=3. also known as cardinal number of a finite set.
**Number of elements in cartesian product of sets :** if two set A={1, 2, 3) and set B={5, 4) then cartesian product of A and B is A*B and number of element in the cartesian product is n(A*B)=n(A)*n(B).

Number of elements in cartesian product A*B=Number of elements in set A * Number of elements in set B

### Cartesian product representation by arrow diagrams

cartesian product of any sets can be represented by arrow diagram where product of each element of one set to each element of another set is drown through arrow line.