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

Options

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

Explanation

To solve the problem, we need to analyze the statement "If \( p \) implies \( (q \lor r) \) is false," and determine the truth values of \( p \), \( q \), and \( r \).

### Step-by-step Solution:

1. **Understanding the Implication**:
The statement \( p \implies (q \lor r) \) is false only when \( p \) is true and \( (q \lor r) \) is false. The implication \( A \implies B \) is false only in the case where \( A \) is true and \( B \) is false.

2. **Finding when \( (q \lor r) \) is false**:
The expression \( (q \lor r) \) (which means \( q \) or \( r \)) is false only when both \( q \) and \( r \) are false. Therefore, we have:
- \( q = \text{false} \)
- \( r = \text{false} \)

3. **Determining the value of \( p \)**:
Since we established that \( (q \lor r) \) is false, for \( p \implies (q \lor r) \) to be false, \( p \) must be true. Thus:
- \( p = \text{true} \)

4. **Final Truth Values**:
From the above deductions, we find:
- \( p = \text{true} \)
- \( q = \text{false} \)
- \( r = \text{false} \)

### Conclusion:
The truth values of \( p \), \( q \), and \( r \) are:
- \( p = \text{true} \)
- \( q = \text{false} \)
- \( r = \text{false} \)