The negation of `qvv(p^^r)` is

Options

A. `~q^^(-p^^-r)`
B. `~q^^(p^^r)`
C. `~qvv(p^^r)`
D. none of these

Explanation

To find the negation of the expression \( q \lor (p \land r) \), we will use De Morgan's laws and the properties of negation in logical expressions.

### Step-by-Step Solution:

1. **Identify the Expression**: The original expression we need to negate is \( q \lor (p \land r) \).

2. **Apply Negation**: We start by applying the negation to the entire expression:
\[ \neg(q \lor (p \land r)) \]

3. **Use De Morgan's Law**: According to De Morgan's laws, the negation of a disjunction is the conjunction of the negations. Therefore, we can rewrite the expression as:
\[ \neg q \land \neg(p \land r) \]

4. **Negate the Conjunction**: Now we need to negate the conjunction \( p \land r \). Again, using De Morgan's laws, we have:
\[ \neg(p \land r) = \neg p \lor \neg r \]

5. **Combine the Results**: Now we substitute back into our expression:
\[ \neg q \land (\neg p \lor \neg r) \]

6. **Final Expression**: The final expression for the negation of \( q \lor (p \land r) \) is:
\[ \neg q \land (\neg p \lor \neg r) \]

### Final Answer:
\[ \neg q \land (\neg p \lor \neg r) \]