Write 'T' for True and 'F' for False.
If p is false and q is true, then: `~| (p ^^ q)` is true.

Answer

To determine the truth value of the statement `~(p ∧ q)` given that \( p \) is false and \( q \) is true, we will follow these steps:

1. **Identify the values of p and q**:
- We know from the problem statement that \( p \) is false (F) and \( q \) is true (T).

2. **Write the expression**:
- The expression we need to evaluate is `~(p ∧ q)`.

3. **Evaluate the conjunction (p ∧ q)**:
- The conjunction \( p ∧ q \) means "p and q". For this conjunction to be true, both \( p \) and \( q \) must be true.
- Since \( p \) is false (F) and \( q \) is true (T), the conjunction \( p ∧ q \) evaluates to false (F).

4. **Apply negation to the result**:
- Now we need to apply negation to the result of the conjunction. The negation of false is true.
- Therefore, `~(p ∧ q)` evaluates to true (T).

5. **Conclusion**:
- Since we have evaluated `~(p ∧ q)` to be true, we conclude that the statement is true.

Thus, the answer is **T** (True).