Question:
In propositional logic \( P ↔ Q \) is equivalent to \( \sim \) (denotes NOT) _______.
In propositional logic \( P ↔ Q \) is equivalent to \( \sim \) (denotes NOT) _______.
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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.
Updated On: Jun 16, 2025
- \( \sim (P \lor Q) \land \sim (Q \lor P) \)
- \( (\sim P \lor Q) \land (\sim Q \lor P) \)
- \( (P \lor Q) \land (Q \lor P) \)
- \( (\sim P \lor Q) \rightarrow (\sim Q \lor P) \)
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The Correct Option is B
Solution and Explanation
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).
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