Question

Which one of the following Boolean expression is a tautology?

• A. $(P\vee q)\wedge (\sim p\vee \sim q)$
• B. $(P\wedge q)\vee (p\vee \sim q)$
• C. $(P\vee q)\wedge (p\vee \sim q)$
• D. $(P\vee q)\vee (p\vee \sim q)$

Answer 1

The correct option is D $(P\vee q)\vee (p\vee \sim q)$

(1) $(P\vee q)\wedge (\sim p\vee \sim q)\equiv (p\vee q)\wedge \sim (p\wedge q)\to$
Not tautology (Take both $p$ and $q$ as $T$)
(2) $(p\wedge q)\vee (p\wedge \sim q)\equiv p\wedge (q\vee \sim q)\equiv p\wedge t\equiv p$
(3) $(p\wedge q)\wedge (p\vee \sim q)\equiv p\vee (q\wedge \sim q)\equiv p\vee c\equiv p$
(4) $(p\vee q)\vee (p\vee \sim q)\equiv p\vee (q\vee \sim q)\equiv p\vee t\equiv t$