Which of the following connectives satisfy commutatiive law ?

Options

A. ` ^^ `
B. ` vv`
C. ` harr`
D. `all the above

Answer

To determine which of the given connectives satisfy the commutative law, we first need to understand what the commutative law states.

### Step-by-step Solution:

1. **Understanding Commutative Law**:
The commutative law states that the order of the operands does not affect the result of the operation. In logical terms, for any two propositions \( p \) and \( q \):
- \( p \lor q \) (logical OR) is equivalent to \( q \lor p \)
- \( p \land q \) (logical AND) is equivalent to \( q \land p \)

2. **Identifying Connectives**:
The common logical connectives include:
- Disjunction (OR, denoted as \( \lor \))
- Conjunction (AND, denoted as \( \land \))
- Implication (denoted as \( \rightarrow \))
- Biconditional (denoted as \( \leftrightarrow \))

3. **Checking Each Connective**:
- **Disjunction (OR)**:
\[ p \lor q \equiv q \lor p \quad \text{(satisfies commutative law)} \]
- **Conjunction (AND)**:
\[ p \land q \equiv q \land p \quad \text{(satisfies commutative law)} \]
- **Implication**:
\[ p \rightarrow q \not\equiv q \rightarrow p \quad \text{(does not satisfy commutative law)} \]
- **Biconditional**:
\[ p \leftrightarrow q \equiv q \leftrightarrow p \quad \text{(satisfies commutative law)} \]

4. **Conclusion**:
The connectives that satisfy the commutative law are:
- Disjunction (OR)
- Conjunction (AND)
- Biconditional

Thus, the answer to the question is that the connectives that satisfy the commutative law are Disjunction, Conjunction, and Biconditional.