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Mathematical Reasoning
medium
Let the operations $*, \odot \in\{\wedge, \vee\}$. If $( p * q ) \odot( p \odot \sim q )$ is a tautology, then the ordered pair $(*, \odot)$ is.
A
$(\vee, \wedge)$
B
$(\vee, \vee)$
C
$(\wedge, \wedge)$
D
$(\wedge, \vee)$
(JEE MAIN-2022)
Solution
Well check each option
For A $\pi=\operatorname{vof} 0=\Lambda$
$( pvq ) \wedge( pv \sim q )$
$\equiv p v(q \wedge \sim q)$
$\equiv p v(c) \equiv p$
For $B :{ }^{*}= v , O = v$
$($ pvq $) \vee($ pv $\sim q ) \equiv t \quad$ using Venn Diagrams
Standard 11
Mathematics
