Cartesian Product of 3 Sets

Last updated at April 16, 2024 by

Let us take set A = {2, 3}

A × A × A = {2, 3} × {2, 3} × {2, 3}

   

Element

1 st element

{ 2 , 3} × { 2 , 3} × { 2 , 3}

(2, 2, 2)

2 nd element

{ 2 , 3} × { 2 , 3} × {2, 3 }

(2, 2, 3)

3 rd element

{ 2 , 3} × {2, 3 } × { 2 , 3}

(2, 3, 2)

4 th element

{ 2 , 3} × {2, 3 } × {2, 3 }

(2, 3, 3)

5 th element

{2, 3 } × { 2 , 3} × { 2 , 3}

(3, 2, 2)

6 th element

{2, 3 } × { 2 , 3} × {2, 3 }

(3, 2, 3)

7 th element

{2, 3 } × {2, 3 } × { 2 , 3}

(3, 3, 2)

8 th element

{2, 3 } × {2, 3 } × {2, 3 }

(3, 3, 3)

∴ A × A × A = {(2, 2, 2), (2, 2, 3), (2, 3, 2), (2, 3, 3), (3, 2, 2), (3, 2, 3), (3, 3, 2), (3, 3, 3)}

 

Note:

A × A × A = {(a,  b,  c) :  a,  b,  c ∈ A}.

Here (a,  b,  c) is called an  ordered triplet

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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 and Computer Science at Teachoo