Enter Set A

Enter Set B

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Answer

↓Steps Explained:↓

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:

Set up an ordered pair using all elements of B {6,7,8,9,10}, with {1}

(1,6)

(1,7)

(1,8)

(1,9)

(1,10)

Ordered pair setup:

Set up an ordered pair using all elements of B {6,7,8,9,10}, with {2}

(2,6)

(2,7)

(2,8)

(2,9)

(2,10)

Ordered pair setup:

Set up an ordered pair using all elements of B {6,7,8,9,10}, with {3}

(3,6)

(3,7)

(3,8)

(3,9)

(3,10)

Ordered pair setup:

Set up an ordered pair using all elements of B {6,7,8,9,10}, with {4}

(4,6)

(4,7)

(4,8)

(4,9)

(4,10)

Ordered pair setup:

Set up an ordered pair using all elements of B {6,7,8,9,10}, with {5}

(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)}

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