Which one of the following Boolean expressions is a tautology?
Show Hint
- \((p \vee q) \wedge (\sim p \vee \sim q)\)
- \((p \vee q) \vee (p \vee \sim q)\)
- \((p \wedge q) \vee (p \wedge \sim q)\)
- \((p \vee q) \wedge (p \vee \sim q)\)
The Correct Option is B
Solution and Explanation
Option (1): \((p \vee q)\wedge(\sim p \vee \sim q)\) is the exclusive-or of \(p, q\); it is false when \(p = q = T\).
Option (3): \((p \wedge q) \vee (p \wedge \sim q) = p \wedge (q \vee \sim q) = p\), not a tautology.
Option (4): \((p \vee q)\wedge(p \vee \sim q) = p \vee (q \wedge \sim q) = p\), not a tautology.
Answer: (2) \((p \vee q) \vee (p \vee \sim q)\)
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