Given set A {1,2,3,4,5}
set B {6,7,8,9,10}
Calculate the Cartesian Product A × B
Cartesian Product Definition:
A × B
Set of all possible:
ordered pairs (a, b)
Calculate the cardinality of A × B
Number of set elements
For set A, we have |A|
For set B, we have |B|
Therefore, |A × B| = |A| · |B|
|A × B| = 5 · 5
|A × B| = 25
Show ordered pair grid:
| 6 | 7 | 8 | 9 | 10 | |
| 1 | (1, 6) | (1, 7) | (1, 8) | (1, 9) | (1, 10) |
| 2 | (2, 6) | (2, 7) | (2, 8) | (2, 9) | (2, 10) |
| 3 | (3, 6) | (3, 7) | (3, 8) | (3, 9) | (3, 10) |
| 4 | (4, 6) | (4, 7) | (4, 8) | (4, 9) | (4, 10) |
| 5 | (5, 6) | (5, 7) | (5, 8) | (5, 9) | (5, 10) |
Ordered pair setup:
(1,6)
(1,7)
(1,8)
(1,9)
(1,10)
Ordered pair setup:
(2,6)
(2,7)
(2,8)
(2,9)
(2,10)
Ordered pair setup:
(3,6)
(3,7)
(3,8)
(3,9)
(3,10)
Ordered pair setup:
(4,6)
(4,7)
(4,8)
(4,9)
(4,10)
Ordered pair setup:
(5,6)
(5,7)
(5,8)
(5,9)
(5,10)
Final Answer
{(1,6),(1,7),(1,8),(1,9),(1,10),(2,6),(2,7),(2,8),(2,9),(2,10),(3,6),(3,7),(3,8),(3,9),(3,10),(4,6),(4,7),(4,8),(4,9),(4,10),(5,6),(5,7),(5,8),(5,9),(5,10)}
