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Mathematical Reasoning
medium
The Boolean expression $\left(\sim\left(p^{\wedge} q\right)\right) \vee q$ is equivalent to
A
$q \rightarrow\left(p^{\wedge} q\right)$
B
$p \rightarrow q$
C
$p \rightarrow(p \vee q)$
D
$p \rightarrow(p \rightarrow q)$
(JEE MAIN-2022)
Solution
$\left(\sim\left( p ^{\wedge} q \right)\right) \vee q$
$=(\sim p \vee \sim q ) \vee q$
$=\sim p \vee \sim q \vee q$
$=\sim p \vee t$
$=$ this statement is a tautology option $D$
$p \Rightarrow( p \vee q )$ is also a tautology.
OR
| $p$ | $q$ | $P ^{\wedge} q$ | $\sim\left( p ^{\wedge} q \right)$ | $\sim\left( p ^{\wedge} q \right) \vee q$ | $p \vee$ $q$ | $p-\{p \vee q)$ |
| $T$ | $T$ | $T$ | $F$ | $T$ | $T$ | $T$ |
| $T$ | $F$ | $F$ | $T$ | $T$ | $T$ | $T$ |
| $F$ | $T$ | $F$ | $T$ | $T$ | $T$ | $T$ |
| $F$ | $F$ | $F$ | $T$ | $T$ | $F$ | $T$ |
Standard 11
Mathematics
