Assertion (A): Gamma rays are electromagnetic waves having the smallest wavelength.
Reason (R): Gamma rays are having the lowest frequency.

Options

A. Both A and R are true and R is the correct explanation of A.
B. Both A and R are true and R is NOT the correct explanation of A.
C. A is true but R is false
D. A is false and R is true

Explanation

To solve the given question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "Gamma rays are electromagnetic waves having the smallest wavelength."
- This statement is indeed **true**. Gamma rays are part of the electromagnetic spectrum and have wavelengths that are on the order of \(10^{-12}\) meters, which is significantly smaller than the wavelengths of other types of electromagnetic waves (like X-rays, ultraviolet, visible light, etc.).

2. **Understanding the Reason (R)**:
- The reason states that "Gamma rays are having the lowest frequency."
- This statement is **false**. In fact, gamma rays have the highest frequency among all electromagnetic waves. The relationship between wavelength and frequency is given by the equation:
\[ c = \lambda \cdot f \]
where \(c\) is the speed of light, \(\lambda\) is the wavelength, and \(f\) is the frequency. Since gamma rays have the smallest wavelength, they must have the highest frequency.

3. **Conclusion**:
- Since the assertion is true and the reason is false, we can conclude that the correct answer is that the assertion is true but the reason is false.

### Final Answer:
- The correct option is: **C: A is true but R is false.**