Question

Which set includes rational numbers but not natural numbers? NOTE: There is a check answer button in the bottom right corner. Click this to check your answer before moving on to the next question. It will not tell you the correct answer, but it will tell you if the answer you selected is correct. You can use this feature once per question.(1 point)Responses0, 1, 2, 30, 1, 2, 3−5, −4, 4, 5−5, −4, 4, 5−623, −2, 511, 78−623, −2, 511, 7834, 456, 185, 8

Answer 1

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

1. Natural Numbers: The set of positive integers (1, 2, 3, ...).
2. Rational Numbers: Numbers that can be expressed as a fraction of two integers (i.e., numbers of the form a/b, where a and b are integers and b ≠ 0).

Now, let's analyze each response:

1. Set 1: 0, 1, 2, 3

   • This set includes natural numbers (1, 2, 3) and also includes 0, which is not a natural number. Nevertheless, it does not meet the requirement as it contains natural numbers.

2. Set 2: −5, −4, 4, 5

   • This set includes only negative and positive integers but does not include any natural numbers (1, 2, etc.). All elements are rational numbers.

3. Set 3: −6, 23, −2, 511, 78

   • This set includes integers that are negative, positive, and also includes 78, which is a natural number. Thus, it does not satisfy the requirement.

4. Set 4: −6, 23, −2, 511, 78

   • This is a repeat of Set 3, hence the same reasoning applies.

5. Set 5: 34, 456, 185, 8

   • This set contains positive integers (34, 456, 185, and 8), which are all natural numbers. Therefore, this set does not meet the requirement.

Among these options, Set 2: −5, −4, 4, 5 is the correct choice as it includes rational numbers yet contains no natural numbers.

So the answer is Set 2: −5, −4, 4, 5.