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

Options

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

Explanation

To solve the problem, we need to analyze the statement given and determine the truth values of \( p \), \( q \), and \( r \) based on the condition that \( p \to q \) (where \( q \lor r \) is false).

### Step-by-step Solution:

1. **Understanding the Implication**:
The statement \( p \to q \) can be interpreted as "if \( p \) is true, then \( q \) must also be true." The implication \( p \to q \) is only false when \( p \) is true and \( q \) is false. Therefore, for \( p \to q \) to be false, we have:
- \( p = \text{True} \)
- \( q = \text{False} \)

2. **Analyzing the Disjunction**:
The expression \( q \lor r \) is given to be false. A disjunction (OR operation) is false only when both operands are false. Therefore, we have:
- \( q = \text{False} \)
- \( r = \text{False} \)

3. **Summarizing the Truth Values**:
From the above analysis, we can summarize the truth values:
- \( p = \text{True} \)
- \( q = \text{False} \)
- \( r = \text{False} \)

### Conclusion:
The truth values of \( p, q, r \) are respectively \( \text{True}, \text{False}, \text{False} \).