State whether the given statements are true or false
The dual of `(p wedge q) vee ~q` is `(p vee q) wedge ~q`

Answer

To determine whether the statement "The dual of `(p wedge q) vee ~q` is `(p vee q) wedge ~q`" is true or false, we need to understand the concept of duality in propositional logic.

### Step-by-Step Solution:

1. **Identify the Original Expression**: The original expression is `(p wedge q) vee ~q`.

2. **Understanding Duality**: In propositional logic, the dual of a statement is obtained by interchanging the logical operators:
- Replace `AND` (∧) with `OR` (∨)
- Replace `OR` (∨) with `AND` (∧)

3. **Apply Duality to the Original Expression**:
- The original expression is `(p wedge q) vee ~q`.
- The dual of `p wedge q` is `p vee q`.
- The dual of `vee ~q` is `wedge ~q`.
- Therefore, applying duality to the entire expression gives us: `p vee q wedge ~q`.

4. **Compare with the Given Statement**: The given statement claims that the dual of `(p wedge q) vee ~q` is `(p vee q) wedge ~q`.
- After applying duality, we found that the dual is indeed `(p vee q) wedge ~q`.

5. **Conclusion**: Since the dual we derived matches the given statement, we conclude that the statement is **True**.

### Final Answer:
The statement "The dual of `(p wedge q) vee ~q` is `(p vee q) wedge ~q`" is **True**.