Question

Which set includes rational numbers but not natural numbers?(1 point)Responses−1, −6, 3, 8−1, −6, 3, 8623, −5, 45, 27623, −5, 45, 2714, −456, 187, 214, −456, 187, 20, 1, 2, 3

Answer 1

To identify the set that includes rational numbers but not natural numbers, we first need to understand the definitions:

- **Natural numbers** are the set of positive integers starting from 1 (i.e., 1, 2, 3, ...).
- **Rational numbers** include all numbers that can be expressed as a fraction of two integers, which means they can be positive, negative, or zero.

Now, let's evaluate each of the provided sets:

1. **Set 1: -1, -6, 3, 8**
- This set includes negative numbers and the positive natural number 3 and 8. Hence, it contains natural numbers.

2. **Set 2: -1, -6, 3, 86**
- Similar to the first set, it includes negative numbers and positive natural numbers (3 and 86). Hence, it contains natural numbers.

3. **Set 3: 23, -5, 45, 276**
- This set contains the natural number 23 and also includes a negative number (-5). Hence, it contains natural numbers.

4. **Set 4: -456, 187, 214**
- This set only includes negative and positive rational numbers, but **does not include any natural numbers** (there are no positive integers starting from 1).

5. **Set 5: -456, 187, 20, 1, 2, 3**
- This set includes the natural numbers 1, 2, and 3. Hence, it contains natural numbers.

Thus, the only set that includes rational numbers but not natural numbers is **Set 4: -456, 187, 214**.