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  4. Let the operations *, odot ∈ ∧, ∨ . If (p * q) odot(p odot ∼ q) is a tautology, then the ordered pair (*, odot) is :

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Q. Let the operations $*, \odot \in\{\wedge, \vee\}$. If $(p * q) \odot(p \odot \sim q)$ is a tautology, then the ordered pair $(*, \odot)$ is :

JEE MainJEE Main 2022Mathematical Reasoning

Solution:

Well check each option
For A $\pi=\operatorname{vof} 0=\Lambda$
$ ( pvq ) \wedge( pv \sim q )$
$ \equiv pv ( q \wedge \sim q ) $
$\equiv pv ( c ) \equiv p$
For $B : * =v, O=v$
$( pvq ) \vee( pv \sim q ) \equiv t$ using Venn Diagrams

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