[A]: Radioactive carbon `^(14)C` method is quite accurate for relatively recent fossils, not older than 40,000 years.
[R]: It was discovered by Libby.

Options

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

Answer

To solve the question regarding the radioactive carbon method and its discovery, we can break it down into a few steps:

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that the radioactive carbon method `^(14)C` is accurate for dating relatively recent fossils, specifically those not older than 40,000 years.
- This is true because the half-life of carbon-14 is about 5,730 years, making it effective for dating organic materials up to around 40,000 years old.

2. **Understanding the Reason (R)**:
- The reason states that the radioactive carbon dating method was discovered by Willard Libby.
- This is also true; Willard Libby developed the carbon-14 dating technique in the late 1940s.

3. **Analyzing the Relationship Between A and R**:
- While both statements A and R are true, we need to determine if R is a correct explanation of A.
- The reason (R) explains who discovered the method, but it does not explain why the method is only accurate for fossils not older than 40,000 years. Therefore, R does not provide a causal relationship to support A.

4. **Conclusion**:
- Both A and R are true, but R is not a correct explanation of A. Thus, the correct answer is that both statements are true, but R does not explain A.

### Final Answer:
Both A and R are true, but R is not a correct explanation of A.

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