If p`rarr` (~p`vv`~q) is false, then the truth values of p and q are respectively.

Options

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

Answer

To solve the problem, we need to analyze the expression \( p \rightarrow (\neg p \lor \neg q) \) and determine when it is false.

### Step-by-Step Solution:

1. **Understanding the Implication**: The implication \( p \rightarrow (\neg p \lor \neg q) \) can be rewritten in terms of truth values. An implication \( A \rightarrow B \) is false only when \( A \) is true and \( B \) is false.

2. **Identifying Components**:
- Let \( A = p \)
- Let \( B = \neg p \lor \neg q \)

3. **Condition for Falsehood**: For \( p \rightarrow (\neg p \lor \neg q) \) to be false:
- \( p \) must be true (i.e., \( A \) is true).
- \( \neg p \lor \neg q \) must be false (i.e., \( B \) is false).

4. **Analyzing \( B \)**: The expression \( \neg p \lor \neg q \) is false when both \( \neg p \) and \( \neg q \) are false. This occurs when:
- \( \neg p \) is false, which means \( p \) is true.
- \( \neg q \) is false, which means \( q \) is true.

5. **Conclusion**:
- From the above analysis, we find that for \( p \rightarrow (\neg p \lor \neg q) \) to be false, both \( p \) and \( q \) must be true.

Thus, the truth values of \( p \) and \( q \) are:
- \( p = \text{True} \)
- \( q = \text{True} \)

### Final Answer:
The truth values of \( p \) and \( q \) are respectively True and True.