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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
