Question:
Which one of the following Boolean expressions is a tautology ?
Correct Option: , 4
Solution:
(1) $(p \vee q) \wedge(\sim p \vee \sim q) \equiv(p \vee q) \wedge \sim(p \wedge q) \rightarrow$
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) $(p \vee q) \vee(p \vee \sim q) \equiv p \vee(q \vee \sim q) \equiv p \vee t \equiv t$