Which set includes rational numbers but not natural numbers?

Question

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(1 point)
Responses

−5, −4, 4, 5
−5, −4, 4, 5

0, 1, 2, 3
0, 1, 2, 3

−623, −2, 511, 78
−623, −2, 511, 78

34, 456, 185, 8

Answer 1

To identify the set that includes rational numbers but not natural numbers, let's first break down the definitions:

• Natural numbers are the positive integers (1, 2, 3, ...).
• Rational numbers include all integers, fractions, and finite or repeating decimals.

From the options given, we need to find a set that includes rational numbers but does not include any natural numbers.

1. −5, −4, 4, 5: This set includes the rational numbers −5, −4, 4, and 5. It also includes natural numbers (4 and 5). So this does not meet the criteria.

2. 0, 1, 2, 3: This set includes the natural numbers (1, 2, 3) and zero, which is a rational number. It does not meet the criteria since it includes natural numbers.

3. −623, −2, 511, 78: This set includes rational numbers (all integers), including −623, −2, 511, and 78. It does contain the natural number 511. So this does not meet the criteria.

4. 34, 456, 185, 8: This set includes rational numbers that are also natural numbers (34, 456, 185, and 8). So this does not meet the criteria.

None of the sets provided clearly contains only rational numbers and not any natural numbers. The correct answer should ideally be a set containing only negative integers or fractions for it to be rational and not include any natural numbers. Please double-check if any options could potentially represent that requirement.