Write the negative of the compound proposition `p vv(~pvvq)`

Answer

To find the negative of the compound proposition \( p \lor (\neg p \lor q) \), we will follow these steps:

### Step 1: Write the given proposition
The given compound proposition is:
\[ p \lor (\neg p \lor q) \]

### Step 2: Apply negation
We need to find the negation of the entire proposition:
\[ \neg (p \lor (\neg p \lor q)) \]

### Step 3: Apply De Morgan's Law
According to De Morgan's Law, the negation of a disjunction is the conjunction of the negations:
\[ \neg (p \lor (\neg p \lor q)) = \neg p \land \neg (\neg p \lor q) \]

### Step 4: Apply De Morgan's Law again
Now we need to negate the inner disjunction:
\[ \neg (\neg p \lor q) = \neg (\neg p) \land \neg q = p \land \neg q \]

### Step 5: Combine the results
Now we can combine the results from Step 3 and Step 4:
\[ \neg (p \lor (\neg p \lor q)) = \neg p \land (p \land \neg q) \]

### Step 6: Simplify the expression
This can be simplified further:
\[ \neg p \land p \land \neg q \]
Since \( \neg p \land p \) is always false (a contradiction), the entire expression simplifies to:
\[ \text{False} \land \neg q = \text{False} \]

### Final Answer
Thus, the negative of the compound proposition \( p \lor (\neg p \lor q) \) is:
\[ \text{False} \]