If `p rarr (p wedge ~ q)` is false. Truth value of p & q will be

Options

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

Answer

To solve the problem, we need to determine the truth values of \( p \) and \( q \) given that the expression \( p \rightarrow (p \wedge \neg q) \) is false.

### Step-by-Step Solution:

1. **Understanding Implication**: The expression \( p \rightarrow (p \wedge \neg q) \) is false only when \( p \) is true and \( (p \wedge \neg q) \) is false. This is because an implication \( A \rightarrow B \) is false only when \( A \) is true and \( B \) is false.

2. **Setting Up the Condition**: For \( (p \wedge \neg q) \) to be false, at least one of the components \( p \) or \( \neg q \) must be false. Since we already established that \( p \) is true, it follows that \( \neg q \) must be false.

3. **Determining \( q \)**: If \( \neg q \) is false, then \( q \) must be true (since negation flips the truth value).

4. **Conclusion**: Thus, we have:
- \( p = \text{True} \)
- \( q = \text{True} \)

### Final Answer:
The truth values of \( p \) and \( q \) are:
- \( p = \text{True} \)
- \( q = \text{True} \)