Question

Which statement is true about the relationships between the number sets?
Responses

Not all natural numbers are real numbers.
Not all natural numbers are real numbers. - no response given

All rational numbers are also integers.
All rational numbers are also integers. - no response given

Some irrational numbers are also integers.
Some irrational numbers are also integers. - no response given

Whole numbers include all natural numbers and 0.

Answer 1

Let's analyze the statements one by one:

1. **Not all natural numbers are real numbers.**
- This statement is **false**. All natural numbers are indeed real numbers.

2. **All rational numbers are also integers.**
- This statement is **false**. While all integers are rational numbers (since they can be expressed as a fraction with a denominator of 1), not all rational numbers are integers (for example, 1/2 is a rational number but not an integer).

3. **Some irrational numbers are also integers.**
- This statement is **false**. By definition, irrational numbers cannot be expressed as fractions of integers, and therefore cannot be integers.

4. **Whole numbers include all natural numbers and 0.**
- This statement is **true**. Whole numbers are defined as the set of natural numbers (1, 2, 3, ...) along with 0.

Based on this analysis, the true statement is: **Whole numbers include all natural numbers and 0.**