Before learning the definition of a Cartesian product, lets refresh our basics.

**Set :**** **A well-defined collection of objects is called a set.

Example:

A={Tom, Dick, Harry}

B={1,2,3,4,5}

Here A and B are two sets. Tom, Dick and Harry are elements of A and 1,2,3,4,5 are the elements of B.

**Pair: **A set having two elements is called a pair.

Example:

(1,2), (2,1)

**Ordered Pair**Ordered pairs are a set having two elements, where the numbers are written in a particular order. The ordered pair with the first element x and second element y is written as (x, y).

(x, y) and (y, x) represent different ordered pairs unless x = y.

**Cartesian Product****The Cartesian product of two sets A and B, denoted by A x B is defined as the collection of all ordered pairs (a, b) such that 'a' is an element of A and 'b' is the element of B.**

In set theoretic notation, the Cartesian product is given by

A x B = {(a, b) | a $\epsilon$ A, b $\epsilon$ B}### Examples on Cartesian Product

Example 1:

Let A = {1,2,3} and B={a, b, c}

Then A x B={(1,a), (1,b), (1,c), (2,a), (2,b), (2,c), (3,a), (3,b), (3,c)}

Example 2:

Let A = {Book, Pen, Pencil} and B={1,2}

Then A x B ={(Book, 1), (Book, 2), (Pen, 1), (Pen, 2), (Pencil, 1), (Pencil, 2)}