Write 'T' for True and 'F' for False.
`p ^^ (p implies q) = q` is under the law of detachment.

Answer

To determine whether the statement `p ^^ (p implies q) = q` is under the law of detachment, we will analyze the components of the statement step by step.

### Step-by-Step Solution:

1. **Understanding the Law of Detachment**:
- The law of detachment states that if we have two premises:
1. \( p \implies q \) (If p, then q)
2. \( p \) (p is true)
- Then we can conclude \( q \) (q is true).

2. **Identifying the Components**:
- The expression we need to analyze is \( p \land (p \implies q) \).
- Here, \( p \land (p \implies q) \) means both \( p \) is true and \( p \implies q \) is true.

3. **Rewriting the Expression**:
- We can rewrite the expression \( p \land (p \implies q) \) in a more logical format.
- According to the law of detachment, if both \( p \) and \( p \implies q \) are true, then \( q \) must also be true.

4. **Evaluating the Expression**:
- If we assume \( p \) is true, then \( p \implies q \) must also be true for the law of detachment to apply.
- Therefore, if both \( p \) and \( p \implies q \) are true, we conclude that \( q \) is true.

5. **Final Conclusion**:
- Thus, we can conclude that \( p \land (p \implies q) \) logically leads to \( q \).
- Therefore, the statement \( p \land (p \implies q) = q \) holds true under the law of detachment.

6. **Truth Value**:
- Since the statement is true, we write 'T' for True.

### Final Answer:
The truth value of the statement `p ^^ (p implies q) = q` is **T** (True).