Question

Let S = {4, 6, 8} and T = {3, 5, 7}. Use the set roster notation to write each of the following sets, and indicate the number of elements that are in each set. (Enter your answers as a comma-separated list of ordered pairs.) (a) S ✕ T S ✕ T = Number of elements in S ✕ T = (b) T ✕ S T ✕ S = Number of elements in T ✕ S = (c) S ✕ S S ✕ S = Number of elements in S ✕ S = (d) T ✕ T T ✕ T = Number of elements in T ✕ T =

Answer 1

Answer:

See explanation

Step-by-step explanation:

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

Given: $S=\{4,6,8\},\ T=\{3,5,7\}$

1. Find $S\times T:$

$S\times T=\{(4,3),(4,5),(4,7),(6,3),(6,5),(6,7),(8,3),(8,5),(8,7)\}$

There are 9 elements.

2. Find $T\times S:$

$T\times S=\{(3,4),(3,6),(3,8),(5,4),(5,6),(5,8),(7,4),(7,6),(7,8)\}$

There are 9 elements.

3. Find $S\times S:$

$S\times S=\{(4,4),(4,6),(4,8),(6,4),(6,6),(6,8),(8,4),(8,6),(8,8)\}$

There are 9 elements.

4. Find $T\times T:$

$T\times T=\{(3,3),(3,5),(3,7),(5,3),(5,5),(5,7),(7,3),(7,5),(7,7)\}$

There are 9 elements.