Question
Which set includes rational numbers but not natural numbers?
A. 1/4, -4 5/6, 18/7, 2
B. 6 2/3, -5, 4/5, 2/7
C. 0, 1, 2, 3
D. -1, -6, 3, 8
A. 1/4, -4 5/6, 18/7, 2
B. 6 2/3, -5, 4/5, 2/7
C. 0, 1, 2, 3
D. -1, -6, 3, 8
Answers
Answer
whats the answer?
Answered by
GPT-4o mini
To find the set that includes rational numbers but not natural numbers, we first define the relevant terms:
- **Rational numbers** are numbers that can be expressed as the quotient of two integers (where the denominator is not zero).
- **Natural numbers** are the set of positive integers starting from 1 (i.e., 1, 2, 3, ...).
Now let's analyze each option:
**A. 1/4, -4 5/6, 18/7, 2**
- \(1/4\) is rational and not a natural number.
- \(-4 5/6\) (which is -4.8333...) is rational and not a natural number.
- \(18/7\) is rational and not a natural number.
- \(2\) is a natural number.
- So this set includes rational numbers and includes 2 as a natural number. **(Not valid)**
**B. 6 2/3, -5, 4/5, 2/7**
- \(6 2/3\) (which is \(6.6667\)) is rational and a natural number.
- \(-5\) is rational and not a natural number.
- \(4/5\) is rational and not a natural number.
- \(2/7\) is also rational and not a natural number.
- So this set includes rational numbers and includes \(6 2/3\) which is a natural number. **(Not valid)**
**C. 0, 1, 2, 3**
- \(0\) is a rational number but not a natural number.
- \(1\), \(2\), and \(3\) are all natural numbers.
- So this set does not qualify as it does not exclude natural numbers. **(Not valid)**
**D. -1, -6, 3, 8**
- \(-1\) is rational and not a natural number.
- \(-6\) is rational and not a natural number.
- \(3\) is a natural number.
- \(8\) is a natural number.
- So this set includes rational numbers, but also includes natural numbers. **(Not valid)**
Upon analysis, none of the options fit the criteria of exclusively containing rational numbers while excluding natural numbers. However, the closest answer among the sets that includes at least some rational numbers while containing non-natural elements is **A. 1/4, -4 5/6, 18/7, 2** if we are asked for rational numbers overall.
If you meant to ask for strictly rational numbers excluding all natural numbers, it appears none of the sets meet that characterization correctly.
- **Rational numbers** are numbers that can be expressed as the quotient of two integers (where the denominator is not zero).
- **Natural numbers** are the set of positive integers starting from 1 (i.e., 1, 2, 3, ...).
Now let's analyze each option:
**A. 1/4, -4 5/6, 18/7, 2**
- \(1/4\) is rational and not a natural number.
- \(-4 5/6\) (which is -4.8333...) is rational and not a natural number.
- \(18/7\) is rational and not a natural number.
- \(2\) is a natural number.
- So this set includes rational numbers and includes 2 as a natural number. **(Not valid)**
**B. 6 2/3, -5, 4/5, 2/7**
- \(6 2/3\) (which is \(6.6667\)) is rational and a natural number.
- \(-5\) is rational and not a natural number.
- \(4/5\) is rational and not a natural number.
- \(2/7\) is also rational and not a natural number.
- So this set includes rational numbers and includes \(6 2/3\) which is a natural number. **(Not valid)**
**C. 0, 1, 2, 3**
- \(0\) is a rational number but not a natural number.
- \(1\), \(2\), and \(3\) are all natural numbers.
- So this set does not qualify as it does not exclude natural numbers. **(Not valid)**
**D. -1, -6, 3, 8**
- \(-1\) is rational and not a natural number.
- \(-6\) is rational and not a natural number.
- \(3\) is a natural number.
- \(8\) is a natural number.
- So this set includes rational numbers, but also includes natural numbers. **(Not valid)**
Upon analysis, none of the options fit the criteria of exclusively containing rational numbers while excluding natural numbers. However, the closest answer among the sets that includes at least some rational numbers while containing non-natural elements is **A. 1/4, -4 5/6, 18/7, 2** if we are asked for rational numbers overall.
If you meant to ask for strictly rational numbers excluding all natural numbers, it appears none of the sets meet that characterization correctly.
Answered by
GPT-4o mini
The set that includes rational numbers but does not include any natural numbers is:
**A. 1/4, -4 5/6, 18/7, 2**
However, this set does contain the natural number \(2\), so it does not meet the criteria of excluding natural numbers entirely.
None of the provided sets strictly meet the requirement of including rational numbers but excluding natural numbers completely. Therefore, if you had to select the set that has the most non-natural numbers among them, the answer would still technically lean toward A, but please note that it includes \(2\) as a natural number.
No set from the listed options completely satisfies the requirement stated in your question. If you are looking for a set that includes only rational numbers and no natural numbers, none of these sets are appropriate.
**A. 1/4, -4 5/6, 18/7, 2**
However, this set does contain the natural number \(2\), so it does not meet the criteria of excluding natural numbers entirely.
None of the provided sets strictly meet the requirement of including rational numbers but excluding natural numbers completely. Therefore, if you had to select the set that has the most non-natural numbers among them, the answer would still technically lean toward A, but please note that it includes \(2\) as a natural number.
No set from the listed options completely satisfies the requirement stated in your question. If you are looking for a set that includes only rational numbers and no natural numbers, none of these sets are appropriate.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.