Question

In propositional logic \( P ↔ Q \) is equivalent to \( \sim \) (denotes NOT) _______.

• A. \( \sim (P \lor Q) \land \sim (Q \lor P) \)
• B. \( (\sim P \lor Q) \land (\sim Q \lor P) \)
• C. \( (P \lor Q) \land (Q \lor P) \)
• D. \( (\sim P \lor Q) \rightarrow (\sim Q \lor P) \)

Hint:

A biconditional statement \( P ↔ Q \) can be rewritten as \( (\sim P \lor Q) \land (\sim Q \lor P) \), which ensures that \( P \) and \( Q \) have the same truth value.

Answer 1

The Correct Option is B

In propositional logic, the biconditional \( P ↔ Q \) is equivalent to the conjunction of two disjunctions: \[ P ↔ Q \equiv (\sim P \lor Q) \land (\sim Q \lor P) \] This equivalence shows that both \( P \) and \( Q \) must have the same truth value for the biconditional to hold true. 
Thus, the correct answer is option (2).