Finding Cartesian Product

Chapter 2 Class 11 Relations and Functions
Concept wise

Let us take two sets A & B

A = {Red, Blue}

B = {Bag, Shirt, Jeans}

Now, how many pairs can we have?

We can have

(Red, Bag), (Red, Shirt) , (Red, Jeans)

and

(Blue, Bag), (Blue, Shirt), (Blue, Jeans)

Cartesian product is the set of all these pairs.

So, we write

A × B = {(Red, Bag), (Red, Shirt) , (Red, Jeans),
(Blue, Bag), (Blue, Shirt), (Blue, Jeans)}

So, definition of Cartesian Product is

For set A & B

A × B = {(a, b): a ∈ A, b ∈ b}

(a, b) is called ordered pair .

Note that:

(a, b) ≠ (b, a)

Let us take some examples

Let A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}

## Find A × B

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

A  × B = {(1, 3), (1, 4),

(2, 3), (2, 4),

(3, 3), (3, 4)}

## Find B × A

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

B × A = { (3, 1), (3, 2), (3, 3),

(4, 1), (4, 2), (4, 3)}

Note that

A × B ≠ B × A

## Find A × C

A = {1, 2, 3}, C = {4, 5, 6}

A × C = {(1, 4), (1, 5), (1, 6),

(2, 4), (2, 5), (2, 6),

(3, 4), (3, 5), (3, 6)}

## Find C × A

C = {4, 5, 6}, A = {1, 2, 3}

C × A = {(4, 1), (4, 2), (4, 3),

(5, 1), (5, 2), (5, 3),

(6, 1), (6, 2), (6, 3), }

Note that

A × C ≠ C × A

## Find B × C

B = {3, 4}, C = {4, 5, 6}

B × C = {(3, 4), (3, 5), (3, 6),

(4, 4), (4, 5), (4, 6)}

## Find C × B

C = {4, 5, 6}, B = {3, 4}

C × B = {(4, 3), (4, 4),

(5, 3), (5, 4),

(6, 3), (6, 4)}

Note that

B × C ≠ C × B

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.