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 ele

Question

1 month ago

3

ments that are in each set?
a. S X T

b. T X S

c. S X S

d. T X T

1 answer:

Svet_ta [12.7K] · Answer 1 · 2026-02-17T03:10:18+03:00

Response:

a. $S\times T=\{(2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(6,1),(6,3),(6,5)\}$ Set S × T consists of 9 elements.

b. $T\times S=\{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)\}$ Set T × S consists of 9 elements.

c. $S\times S=\{(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)\}$ Set S × S contains 9 elements.

d. $T\times T=\{(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)\}$ Set T × T includes 9 elements.

Detailed explanation:

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

The goal is to express each of the sets in set-roster format, indicating the count of elements in each respective set.

a.

$S\times T=\{(s,t)|s\in S and t\in T\}$

$S\times T=\{(2,1),(2,3),(2,5),(4,1),(4,3),(4,5),(6,1),(6,3),(6,5)\}$ Set S × T has 9 elements.

b.

$T\times S=\{(t,s)|s\in S and t\in T\}$

$T\times S=\{(1,2),(1,4),(1,6),(3,2),(3,4),(3,6),(5,2),(5,4),(5,6)\}$ Set T × S has 9 elements.

c.

$S\times S=\{(s,s)|s\in S \}$

$S\times S=\{(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),(6,2),(6,4),(6,6)\}$ Set S × S has 9 elements.

d.

$T\times T=\{(t,t)|t\in T\}$

$T\times T=\{(1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5,1),(5,3),(5,5)\}$ Set T × T has 9 elements.