`(p vv p) hArr p, (p ^^ p) hArr p` are under:

Options

A. Idempotent laws
B. Absorption laws
C. Chain rule
D. Commutative laws.

Answer

To solve the question regarding the logical expressions `(p ∨ p) ↔ p` and `(p ∧ p) ↔ p`, we need to identify which logical law they correspond to. Let's break down the solution step by step.

### Step-by-Step Solution

1. **Understanding the Expressions**:
- The first expression is `(p ∨ p) ↔ p`, which means "p or p is equivalent to p".
- The second expression is `(p ∧ p) ↔ p`, which means "p and p is equivalent to p".

2. **Analyzing the First Expression**:
- According to the **Idempotent Law** in logic, we have:
- \( p \lor p \equiv p \)
- This means that the disjunction (OR operation) of a statement with itself is equivalent to the statement itself.

3. **Analyzing the Second Expression**:
- Similarly, for the conjunction (AND operation), the **Idempotent Law** states:
- \( p \land p \equiv p \)
- This indicates that the conjunction of a statement with itself is also equivalent to the statement itself.

4. **Conclusion**:
- Both expressions `(p ∨ p) ↔ p` and `(p ∧ p) ↔ p` are examples of the **Idempotent Law**.
- Therefore, the answer to the question is that both statements are under the **Idempotent Law**.

### Final Answer
The expressions `(p ∨ p) ↔ p` and `(p ∧ p) ↔ p` are under the **Idempotent Law**.

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