Assertion : Rational number lying between two rational numbers a and b is `a+b//2` .
Reason : There is one rational number lying between any two rational numbers .

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion .
B. If both assertion and reason are true but reason is not the correct explanation of assertion .
C. If assertion is true but reason is false.
D. If assertion is false but reason is true .

Answer

To solve the assertion and reason problem, we need to analyze both statements carefully.

**Step 1: Understanding the Assertion**
The assertion states that a rational number lying between two rational numbers \( a \) and \( b \) can be expressed as \( \frac{a + b}{2} \).

- **Explanation**: This is indeed true because the expression \( \frac{a + b}{2} \) represents the average of the two numbers \( a \) and \( b \). Since \( a \) and \( b \) are rational numbers, their average is also a rational number. Therefore, there is at least one rational number (specifically, the average) between any two rational numbers.

**Step 2: Understanding the Reason**
The reason states that there is only one rational number lying between any two rational numbers.

- **Explanation**: This statement is false. Between any two rational numbers, there are infinitely many rational numbers. For example, between \( 1 \) and \( 2 \), we can find \( 1.5 \), \( 1.25 \), \( 1.75 \), and so on, ad infinitum. Therefore, the claim that there is only one rational number between two rational numbers is incorrect.

**Step 3: Conclusion**
Based on the analysis:
- The assertion is true.
- The reason is false.

Thus, the correct conclusion is that the assertion is true, but the reason is false.

### Final Answer:
- Assertion: True
- Reason: False