State in each case whether true or false:
Some real numbers are rational numbers.

Answer

To determine whether the statement "Some real numbers are rational numbers" is true or false, we can break it down step by step.

### Step 1: Understand the Definitions
- **Real Numbers**: This set includes all the numbers that can be found on the number line. This includes both rational and irrational numbers.
- **Rational Numbers**: These are numbers that can be expressed as a fraction \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \). Examples include \( \frac{1}{2}, 3, -4, 0.75 \), etc.
- **Irrational Numbers**: These are numbers that cannot be expressed as a simple fraction. Their decimal expansions are non-repeating and non-terminating. Examples include \( \sqrt{2}, \pi, e \), etc.

### Step 2: Analyze the Statement
The statement claims that "Some real numbers are rational numbers."

### Step 3: Identify the Relationship
Since real numbers include both rational and irrational numbers, it follows that:
- There are indeed real numbers that are rational. For example, \( 1, -3, \frac{1}{2} \) are all rational numbers and thus are also real numbers.

### Step 4: Conclusion
Since we have established that there are real numbers that are rational, we can conclude that the statement is true.

### Final Answer
**True**: Some real numbers are rational numbers.

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