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Let S = {2,4,6} and T = {1,3,5}. Use the set-roster notation to write each of the following sets, and indicate the number of elements that are in each set?

a. S X T

b. T X S

c. S X S

d. T X T

Respuesta :

Answer:

a. [tex]S\times T=\{(2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(6,1),(6,3),(6,5)\}[/tex] . Set S × T has 9 elements.

b. [tex]T\times S=\{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)\}[/tex]. Set T × S has 9 elements.  

c. [tex]S\times S=\{(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)\}[/tex] . Set S × S has 9 elements.

d. [tex]T\times T=\{(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)\}[/tex] . Set T × T has 9 elements.

Step-by-step explanation:

The given sets are S={2,4,6} and T={1,3,5}.

We need to find the set-roster notation to write each of the following sets, and the number of elements that are in each set.

a.

[tex]S\times T=\{(s,t)|s\in S and t\in T\}[/tex]

[tex]S\times T=\{(2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(6,1),(6,3),(6,5)\}[/tex]

Set S × T has 9 elements.

b.

[tex]T\times S=\{(t,s)|s\in S and t\in T\}[/tex]

[tex]T\times S=\{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)\}[/tex]

Set T × S has 9 elements.  

c.

[tex]S\times S=\{(s,s)|s\in S \}[/tex]

[tex]S\times S=\{(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)\}[/tex]

Set S × S has 9 elements.

d.

[tex]T\times T=\{(t,t)|t\in T\}[/tex]

[tex]T\times T=\{(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)\}[/tex]

Set T × T has 9 elements.

fichoh

Using the set roster notation, the number of elements in each of the sets would be the product of the number of elements in each individual set, which is 9.

  • S = {2, 4, 6}
  • T = {1, 3, 5}

A.) S × T :

{2, 4, 6} × {1, 3, 5}

{(2, 1), (2, 3), (2, 5), (4, 1), (4, 3), (4, 5), (6, 1), (6, 3), (6, 5)}

Number is of elements = 9

B.) T × S :

{1, 3, 5} × {2, 4, 6}

{(1,2), (1,4), (1,6), (3,2), (3,4), (3, 6), (5, 2), (5,4), (5,6)}

Number is of elements = 9

C.) S × S :

{1, 3, 5} × {1, 3, 5}

{(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 3), (5, 1), (5, 3), (5, 5)}

Number is of elements = 9

D.) T × T :

{2, 4,6} × {2, 4, 6}

{(2,2), (2, 4), (2, 6), (4,2), (4, 4), (4, 6), (6,2), (6, 4), (6,6)}

Number is of elements = 9

Hence, the distribution of values of each set.

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