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Mathematical Reasoning
medium
Let $*, \square \in\{\wedge, \vee\}$ be such that the Boolean expression $(\mathrm{p} * \sim \mathrm{q}) \Rightarrow(\mathrm{p} \square \mathrm{q})$ is a tautology. Then :
A
$*=\vee, \square=\vee$
B
$*=\wedge, \square=\wedge$
C
$*=\wedge, \square=\vee$
D
$*=\vee, \square=\wedge$
(JEE MAIN-2021)
Solution
$(\mathrm{p} \wedge \sim \mathrm{q}) \rightarrow(\mathrm{p} \vee \mathrm{q})$ is tautology
| $p$ | $q$ | $\sim \mathrm{q}$ | $\mathrm{p} \wedge \sim \mathrm{q}$ | $\mathrm{p} \vee \mathrm{q}$ | $(\mathrm{p} \wedge \sim \mathrm{q}) \rightarrow(\mathrm{p} \vee \mathrm{q})$ |
| $T$ | $T$ | $F$ | $F$ | $T$ | $T$ |
| $T$ | $F$ | $T$ | $T$ | $T$ | $T$ |
| $F$ | $T$ | $F$ | $F$ | $T$ | $T$ |
| $F$ | $F$ | $T$ | $F$ | $F$ | $T$ |
Standard 11
Mathematics
