The dual of `(p ^^ q) vv r` is .......

Answer

To find the dual of the expression \( (p \land q) \lor r \), we will follow the rules of duality in propositional logic. The duality principle states that conjunctions (AND, represented by \( \land \)) are replaced with disjunctions (OR, represented by \( \lor \)) and vice versa.

### Step-by-Step Solution:

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

2. **Apply Duality Rules**:
- The first operation in the expression is a conjunction \( (p \land q) \). According to the duality principle, we replace this conjunction with a disjunction. Thus, \( p \land q \) becomes \( p \lor q \).
- The second operation is a disjunction \( \lor r \). We replace this disjunction with a conjunction. Thus, \( \lor r \) becomes \( \land r \).

3. **Rewrite the Expression**: After applying the duality rules, we rewrite the expression:
- The original expression \( (p \land q) \lor r \) becomes \( (p \lor q) \land r \).

4. **Final Result**: Therefore, the dual of the expression \( (p \land q) \lor r \) is \( (p \lor q) \land r \).

### Final Answer:
The dual of \( (p \land q) \lor r \) is \( (p \lor q) \land r \).