`~(pvv(~pvvq))` is equal to

Explanation

To solve the expression \( \sim (p \lor \sim p \lor q) \), we will use logical equivalences and De Morgan's laws step by step.

### Step-by-step Solution:

1. **Identify the expression**: We start with the expression \( \sim (p \lor \sim p \lor q) \).

2. **Apply De Morgan's Law**: According to De Morgan's laws, the negation of a disjunction is equivalent to the conjunction of the negations. Therefore, we can rewrite the expression as:
\[ \sim (p \lor \sim p \lor q) = \sim p \land \sim (\sim p \lor q) \]

3. **Negate the inner expression**: Now, we need to apply De Morgan's law again to the inner expression \( \sim (\sim p \lor q) \):
\[ \sim (\sim p \lor q) = \sim (\sim p) \land \sim q = p \land \sim q \]

4. **Combine the results**: Now we can substitute back into our expression:
\[ \sim (p \lor \sim p \lor q) = \sim p \land (p \land \sim q) \]

5. **Simplify the expression**: We can now simplify \( \sim p \land (p \land \sim q) \):
\[ \sim p \land p \land \sim q \]
The term \( \sim p \land p \) is always false (contradiction), which means the entire expression evaluates to false:
\[ \sim p \land p \land \sim q = \text{False} \]

### Final Answer:
Thus, the expression \( \sim (p \lor \sim p \lor q) \) simplifies to **False**.