`p ^^ (q vv r) -= (p ^^ q) vv (p ^^ r)` is :

Options

A. Associative law
B. Distributive
C. Identity law
D. Absorption

Answer

To solve the question \( p \land (q \lor r) \equiv (p \land q) \lor (p \land r) \), we will show that this is an application of the distributive law in propositional logic.

### Step-by-Step Solution:

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

2. **Apply the Distributive Law**:
According to the distributive law in logic, we can distribute \( p \) across the disjunction \( (q \lor r) \). The distributive law states that:
\[ p \land (q \lor r) \equiv (p \land q) \lor (p \land r) \]

3. **Rewrite the Expression**:
Using the distributive law, we rewrite the left-hand side:
\[ p \land (q \lor r) = (p \land q) \lor (p \land r) \]

4. **Conclusion**:
Therefore, we conclude that:
\[ p \land (q \lor r) \equiv (p \land q) \lor (p \land r) \]
This shows that the original expression is indeed true and is an application of the distributive law.

### Final Answer:
The statement \( p \land (q \lor r) \equiv (p \land q) \lor (p \land r) \) is an example of the **Distributive Law**.