Which of the following sets could represent these elements?

$\left\{-2,-1,0,1,2,3 \ldots\right\}$

$\left\{x \mid-2 \leq x \leq 3, x \in W\right\}$

$\left\{x \mid-2 \leq x \leq 3, x \in I \right\}$

$\left\{x \mid-2 \leq x \leq 3, x \in R \right\}$

$\left\{x \mid-2 \leq x, x \in W\right\}$

$\left\{x \mid-2 \leq x, x \in I \right\}$

$\left\{x \mid-2 \leq x, x \in R \right\}$

The problem requires identifying a set equivalent to { − 2 , − 1 , 0 , 1 , 2 , 3 , … } .
Analyze each given set using the definitions of whole numbers (W), integers (I), and real numbers (R).
Compare each set to the target set.
The set { x ∣ − 2 ≤ x , x ∈ I } is equivalent to the given set, so the final answer is { x ∣ − 2 ≤ x , x ∈ I } ​ .

Explanation

Analyzing the Sets We are given the set { − 2 , − 1 , 0 , 1 , 2 , 3 , … } and asked to identify which of the provided sets is equivalent. Let's analyze each option:

{ x ∣ − 2 ≤ x ≤ 3 , x ∈ W } : This represents whole numbers (non-negative integers) between -2 and 3, inclusive. Since whole numbers are non-negative, this set is { 0 , 1 , 2 , 3 } .

{ x ∣ − 2 ≤ x ≤ 3 , x ∈ I } : This represents integers between -2 and 3, inclusive. This set is { − 2 , − 1 , 0 , 1 , 2 , 3 } .

{ x ∣ − 2 ≤ x ≤ 3 , x ∈ R } : This represents real numbers between -2 and 3, inclusive. This is the interval [ − 2 , 3 ] .

{ x ∣ − 2 ≤ x , x ∈ W } : This represents whole numbers greater than or equal to -2. Since whole numbers are non-negative, this set is { 0 , 1 , 2 , 3 , … } .

{ x ∣ − 2 ≤ x , x ∈ I } : This represents integers greater than or equal to -2. This set is { − 2 , − 1 , 0 , 1 , 2 , 3 , … } .

{ x ∣ − 2 ≤ x , x ∈ R } : This represents real numbers greater than or equal to -2. This is the interval [ − 2 , ∞ ) .

Identifying the Correct Set Comparing each of these sets to the given set { − 2 , − 1 , 0 , 1 , 2 , 3 , … } , we see that the set { x ∣ − 2 ≤ x , x ∈ I } matches exactly.

Final Answer Therefore, the correct set is { x ∣ − 2 ≤ x , x ∈ I } .


Examples
Understanding sets and their notations is fundamental in mathematics and computer science. For instance, when defining the domain of a function, we specify the set of possible input values. Similarly, in programming, we use sets to define the types of variables or the possible values they can hold. For example, if you are writing a program that processes age data, you might define the age variable as an integer within a specific range, like the set of integers between 0 and 150, representing possible human ages. This ensures data validity and helps prevent errors in your program.

Answered by GinnyAnswer | 2025-07-03

The sets that correctly represent the elements of { -2, -1, 0, 1, 2, 3, \ldots } are { x \mid -2 \leq x \leq 3, x \in I } and { x \mid -2 \leq x, x \in I }. However, the first option explicitly matches the bounded range, so it is the preferred answer.
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Answered by Anonymous | 2025-07-04