Questions: Choose the correct description of the set. A=3,6,9,12, ... Choose the correct answer below. A. A=x x is a multiple of a natural number and -3 B. A=x x is an odd integer C. A=x x ∈ N and x is a multiple of 3 D. A=

Choose the correct description of the set.
A=3,6,9,12, ...

Choose the correct answer below.
A. A=x x is a multiple of a natural number and -3
B. A=x x is an odd integer
C. A=x x ∈ N and x is a multiple of 3
D. A=

Transcript text: Choose the correct description of the set. $A=\{3,6,9,12, \ldots\}$ Choose the correct answer below. A. $A=\{x \mid x$ is a multiple of a natural number and -3$\}$ B. $A=\{x \mid x$ is an odd integer $\}$ C. $A=\{x \mid x \in N$ and $x$ is a multiple of 3$\}$ D. $A=\{ \}$

Solution

Solution Steps

To determine the correct description of the set $ A = \{3, 6, 9, 12, \ldots\} $, we need to identify the pattern or rule that defines the elements of the set. The elements are multiples of 3, starting from 3. Therefore, the correct description is the set of natural numbers that are multiples of 3.

Step 1: Identify the Set

The set $ A = \{3, 6, 9, 12, \ldots\} $ consists of numbers that are multiples of 3. This can be expressed mathematically as $ A = \{ x \mid x = 3n, n \in \mathbb{N} \} $, where $ \mathbb{N} $ represents the set of natural numbers.

Step 2: Evaluate the Options

We need to evaluate the provided options to find the correct description of the set $ A $:

Option A: $ A = \{ x \mid x \text{ is a multiple of a natural number and } -3 \} $ (Incorrect)
Option B: $ A = \{ x \mid x \text{ is an odd integer} \} $ (Incorrect)
Option C: $ A = \{ x \mid x \in \mathbb{N} \text{ and } x \text{ is a multiple of } 3 \} $ (Correct)
Option D: $ A = \{ \} $ (Incorrect)

Step 3: Confirm the Correct Description

Since the elements of set $ A $ are indeed multiples of 3 and belong to the natural numbers, we confirm that Option C accurately describes the set.