QJEEM22Maa744: JEE Main 2022 Mathematics - Class 11 JEEM22Maa744 Solution: Let the operations . If is a tautology, then the ordered pair…

$* ,\, \odot \in \{ \wedge ,\, \vee \}$

Now for $(p * q) \odot (p \odot \sim q)$ is tautology

(A) $( \vee , \wedge ):(p \vee q) \wedge (p \wedge \sim q)$ not a tautology

(B) $( \vee , \vee ):(p \vee q) \vee (p \vee \sim q)$

$= P \vee T$ is tautology

(C) $( \wedge , \wedge ):(p \wedge q) \wedge (p \wedge \sim q)$

$= (p \wedge p) \wedge (q \wedge \sim q) = p \wedge F$ not a tautology (Fallasy)

(D) $( \wedge , \vee ):(p \wedge q) \vee (p \vee \sim q)$ not a tautology