Enter Set A

Enter Set B


Answer
Success!
{(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)}

↓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:

 678910
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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