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

Answer

To determine whether the statement "All real numbers are rational numbers" is true or false, we can follow these steps:

### 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 numbers (like fractions and integers) and irrational numbers (like √2 and π).
- **Rational Numbers**: These are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. Examples include 1/2, -3, and 4.75.

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

### Step 3: Identify the types of numbers
- Rational numbers are a subset of real numbers.
- Irrational numbers are also part of the real numbers but cannot be expressed as a fraction of two integers.

### Step 4: Conclusion
Since there are numbers (like √2 and π) that are real but not rational, we can conclude that the statement "All real numbers are rational numbers" is **false**.

### Final Answer
**False**: Not all real numbers are rational numbers.

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