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  4. Which one of the following Boolean expressions is a tautology ?

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Q. Which one of the following Boolean expressions is a tautology ?

JEE MainJEE Main 2019Mathematical Reasoning

Solution:

(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) $(p \vee q) \wedge (p \vee \sim q) \equiv p \vee (q \wedge \sim q) \equiv p \vee c \equiv p$
(4) $(p\vee q) \vee (p \vee \sim q) \equiv p \vee(q \vee \sim q) \equiv p \vee t \equiv t$