Write each set in the indicated form. If you need

Questions: Write each set in the indicated form. If you need to use "..." to indicate a pattern, make sure to list at least four elements of the set. (a) Set-builder form: x x is an integer and 4<x<8 Roster form: (b) Roster form: -4,-3,-2,-1, ... Set-builder form:

Transcript text: Write each set in the indicated form. If you need to use "..." to indicate a pattern, make sure to list at least four elements of the set. (a) Set-builder form: $\{x \mid x$ is an integer and $4

Solution

Solution Steps

To convert the given sets between set-builder form and roster form, we need to understand the definitions and constraints provided in each form.

(a) For the set-builder form $\{x \mid x$ is an integer and $4<x<8\}$, we need to list all integers that satisfy the condition $4 < x < 8$.

(b) For the roster form $\{-4,-3,-2,-1, \ldots\}$, we need to describe the set in set-builder notation, which includes all negative integers.

Solution Approach

(a) Convert the set-builder form to roster form by listing all integers between 4 and 8. (b) Convert the roster form to set-builder form by describing the set of all negative integers.

Step 1: Convert Set-Builder Form to Roster Form

For the set-builder form $\{x \mid x \text{ is an integer and } 4 < x < 8\}$, we list all integers that satisfy the condition $4 < x < 8$.

Step 2: Convert Roster Form to Set-Builder Form

For the roster form $\{-4, -3, -2, -1, \ldots\}$, we describe the set in set-builder notation, which includes all negative integers.