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Write each set in the indicated form. If you need to use "..." to indicate a pattern, list at least four elements of the set.

(a) Roster form: [tex]\{0, 1, 2, 3, \ldots\}[/tex]
Set-builder form: [tex]\{x \mid x \text{ is a non-negative integer}\}[/tex]

(b) Set-builder form: [tex]\{y \mid y \text{ is an integer and } -3 \leq y \leq 0\}[/tex]
Roster form: [tex]\{-3, -2, -1, 0\}[/tex]


Sagot :

Let's go through each part of the problem step-by-step.

### Part (a)
We are given a set in roster form, which lists out elements of the set explicitly:

Given Roster Form:
[tex]\[ \{0, 1, 2, 3, \ldots\} \][/tex]

This set includes all non-negative integers starting from 0. To convert this to set-builder form, we need to describe this set using a property that all the elements of the set satisfy.

Set-builder Form:
[tex]\[ \{x \mid x \text{ is an integer and } x \geq 0\} \][/tex]

Explanation: The set-builder notation describes the set containing all integers [tex]\(x\)[/tex] that are greater than or equal to 0.

### Part (b)
We are given a set in set-builder form, which uses a property to define the set:

Given Set-builder Form:
[tex]\[ \{y \mid y \text{ is an integer and } -3 \leq y \leq 0\} \][/tex]

This set includes all integers [tex]\(y\)[/tex] that satisfy the condition [tex]\(-3 \leq y \leq 0\)[/tex]. To convert this to roster form, we need to list out all the elements that satisfy this condition.

Roster Form:
[tex]\[\{-3, -2, -1, 0\}\][/tex]

Explanation: The roster form shows explicitly that the set includes the integers -3, -2, -1, and 0.

### Summary
- Set given in roster form: [tex]\(\{0, 1, 2, 3, \ldots\}\)[/tex]
- Converted to set-builder form: [tex]\(\{x \mid x \text{ is an integer and } x \geq 0\}\)[/tex]

- Set given in set-builder form: [tex]\(\{y \mid y \text{ is an integer and } -3 \leq y \leq 0\}\)[/tex]
- Converted to roster form: [tex]\(\{-3, -2, -1, 0\}\)[/tex]