Question

question 11 (1 point)

use the alternative method to express each set.

\\{x : x \text{ is a letter in \dogged\}\\}

3

\\{d, o, g, g, e, d\\}

4

6

\\{d, o, g\\}

\\{d, e, g, o\\}

Explanation:

🆕 New Concept Discovered: Set-Builder to Roster Form
Listing unique elements without repetition.

Step 1: Identify the letters in the word

The given set is in set-builder notation:

$$ \{x : x \text{ is a letter in "dogged"}\} $$

First, we list all the individual letters that make up the word "dogged":

$$ \text{d, o, g, g, e, d} $$

Step 2: Remove duplicate elements

In set theory, sets do not contain duplicate elements. Each distinct member is listed only once.

We identify the unique letters from our list:

• 'd' (appears twice, keep one)
• 'o' (appears once)
• 'g' (appears twice, keep one)
• 'e' (appears once)

The unique elements are:

$$ \text{d, o, g, e} $$

Step 3: Match with the options

We write these unique elements inside curly braces. The order of elements in a set does not matter:

$$ \{\text{d, e, g, o}\} $$

This matches the last option.

Answer:

$$ \{\text{d, e, g, o}\} $$