If `p to (qvvr)` is false, then the truth values of p,q, and r are, respectively.

Options

A. T,T,F
B. F,F,F
C. F,T,T
D. T,F,F

Explanation

To solve the problem, we need to analyze the statement "p implies (q or r)" and determine the truth values of p, q, and r given that this statement is false.

### Step-by-Step Solution:

1. **Understanding the Implication**:
The statement "p implies (q or r)" can be represented as \( p \rightarrow (q \lor r) \). This statement is false only when p is true and \( (q \lor r) \) is false.

2. **Condition for Falsehood**:
The implication \( p \rightarrow (q \lor r) \) is false if:
- p is true (T)
- \( (q \lor r) \) is false (F)

3. **Analyzing \( (q \lor r) \)**:
The expression \( (q \lor r) \) is false only when both q and r are false. Therefore, we have:
- \( q = F \)
- \( r = F \)

4. **Determining p**:
Since we established that \( p \) must be true for the implication to be false, we have:
- \( p = T \)

5. **Final Truth Values**:
Therefore, the truth values of p, q, and r are:
- \( p = T \) (True)
- \( q = F \) (False)
- \( r = F \) (False)

### Conclusion:
The truth values of p, q, and r are respectively: **True, False, False**.