Which statement is true about the relationships between the number sets.

Question

All integers are also rational numbers.
Some rational numbers are also integers.
Not all natural numbers are real numbers.
Whole numbers include all positive and negative integers.

Answer 1

Let's evaluate each statement about the relationships between the number sets:

1. All integers are also rational numbers.

   • True. An integer can be expressed as a fraction (like \( a = \frac{a}{1} \)) which makes it a rational number.

2. Some rational numbers are also integers.

   • True. Specifically, any integer is a rational number (as stated above), hence at least the integers are included in the set of rational numbers.

3. Not all natural numbers are real numbers.

   • False. All natural numbers (like 1, 2, 3,...) are indeed real numbers.

4. Whole numbers include all positive and negative integers.

   • False. Whole numbers typically include all non-negative integers (like 0, 1, 2, 3,...), but do not include negative integers.

Based on the above evaluations, the true statements are:

• All integers are also rational numbers.
• Some rational numbers are also integers.

The other two statements are false.