Question

a. write the set of letters in the word rollicking using the most concise method where a is the set of lowercase letters. (use a comma to separate answers as needed.) a. the set of letters is {x|x∈a and x = }. b. the set of letters is . b. write the set of natural numbers less than 22 using the most concise method. (use a comma to separate answers as needed.) a. the set of number is {x|x∈n and x = }. b. the set of numbers is {x|x∈n and x > }. c. the set of numbers is {x|x∈n and x < }. d. the set of numbers is .

Explanation:

Part a

Step 1: Identify the word and set A

The word is 'rollicking'. Let's list its letters: r, o, l, i, c, k, i, n, g. Now, set A is lowercase letters. We need to find unique letters (since sets have unique elements). So unique letters: r, o, l, i, c, k, n, g.

Step 2: Write the set

Using set-builder notation, the set of letters in 'rollicking' is $\{x | x \in A \text{ and } x \in \{r, o, l, i, c, k, n, g\}\}$. But more concisely, list the unique letters. Wait, the options: Option A is $\{x|x\in A \text{ and } x = \text{[letters]}\}$? Wait, maybe the word 'rollicking' has letters: let's spell it: r, o, l, l, i, c, k, i, n, g. So unique letters: r, o, l, i, c, k, n, g. So the set is $\{r, o, l, i, c, k, n, g\}$ or in set-builder, $\{x | x \in A \text{ and } x \text{ is a letter in 'rollicking'}\}$. But since the options have A as $\{x|x\in A \text{ and } x = \dots\}$? Wait, maybe the problem is about unique letters. Let's check the word: 'rollicking' has letters: r, o, l, l, i, c, k, i, n, g. So unique letters: r, o, l, i, c, k, n, g. So the set is $\{r, o, l, i, c, k, n, g\}$. But the options: A is $\{x|x\in A \text{ and } x = \dots\}$? Maybe the question is to list the unique letters. So the set of letters is $\{r, o, l, i, c, k, n, g\}$.

Part b

Step 1: Recall natural numbers

Natural numbers $\mathbb{N}$ are typically 1, 2, 3, ... (or sometimes 0,1,2,... but usually positive integers). We need natural numbers less than 22. So $x \in \mathbb{N}$ and $x < 22$. So the set is $\{x | x \in \mathbb{N} \text{ and } x < 22\}$, which is $\{1, 2, 3, \dots, 21\}$ (if $\mathbb{N}$ starts at 1) or $\{0, 1, \dots, 21\}$ (if $\mathbb{N}$ starts at 0). But the options: Option C is $\{x|x\in \mathbb{N} \text{ and } x < \text{[22]}\}$. So the set of natural numbers less than 22 is $\{x | x \in \mathbb{N} \text{ and } x < 22\}$, which can be written as $\{1, 2, \dots, 21\}$ (or including 0 if $\mathbb{N}$ includes 0, but usually less than 22 means up to 21).

Part a Answer (assuming option A is the correct set-builder or listing, but maybe the letters are r, o, l, i, c, k, n, g. So the set is $\{r, o, l, i, c, k, n, g\}$ or in set-builder as per option A.

Part b Answer:

The set of natural numbers less than 22 is $\{x | x \in \mathbb{N} \text{ and } x < 22\}$, which corresponds to Option C (since $x < 22$ and $x \in \mathbb{N}$).

Final Answers:

Part a:

The set of letters in 'rollicking' is $\{r, o, l, i, c, k, n, g\}$ (or in set-builder as per the correct option, likely Option A with the letters filled).

Part b:

Option C: The set of numbers is $\{x|x\in \mathbb{N} \text{ and } x < 22\}$ (or $\{1, 2, \dots, 21\}$ if $\mathbb{N}$ starts at 1).

(Note: The image's options are a bit unclear, but based on standard set problems, for part b, natural numbers less than 22 are $x \in \mathbb{N}, x < 22$, so Option C is correct as it has $x < 22$ and $x \in \mathbb{N}$.)

Answer:

Step 1: Recall natural numbers

Natural numbers $\mathbb{N}$ are typically 1, 2, 3, ... (or sometimes 0,1,2,... but usually positive integers). We need natural numbers less than 22. So $x \in \mathbb{N}$ and $x < 22$. So the set is $\{x | x \in \mathbb{N} \text{ and } x < 22\}$, which is $\{1, 2, 3, \dots, 21\}$ (if $\mathbb{N}$ starts at 1) or $\{0, 1, \dots, 21\}$ (if $\mathbb{N}$ starts at 0). But the options: Option C is $\{x|x\in \mathbb{N} \text{ and } x < \text{[22]}\}$. So the set of natural numbers less than 22 is $\{x | x \in \mathbb{N} \text{ and } x < 22\}$, which can be written as $\{1, 2, \dots, 21\}$ (or including 0 if $\mathbb{N}$ includes 0, but usually less than 22 means up to 21).

Part a Answer (assuming option A is the correct set-builder or listing, but maybe the letters are r, o, l, i, c, k, n, g. So the set is $\{r, o, l, i, c, k, n, g\}$ or in set-builder as per option A.

Part b Answer:

The set of natural numbers less than 22 is $\{x | x \in \mathbb{N} \text{ and } x < 22\}$, which corresponds to Option C (since $x < 22$ and $x \in \mathbb{N}$).

Final Answers:

Part a:

The set of letters in 'rollicking' is $\{r, o, l, i, c, k, n, g\}$ (or in set-builder as per the correct option, likely Option A with the letters filled).

Part b:

Option C: The set of numbers is $\{x|x\in \mathbb{N} \text{ and } x < 22\}$ (or $\{1, 2, \dots, 21\}$ if $\mathbb{N}$ starts at 1).

(Note: The image's options are a bit unclear, but based on standard set problems, for part b, natural numbers less than 22 are $x \in \mathbb{N}, x < 22$, so Option C is correct as it has $x < 22$ and $x \in \mathbb{N}$.)