Q. The Boolean expression $\left(\sim\left(p{\wedge} q\right)\right) \vee q$ is equivalent to :
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.
$OR$
$p$
$q$
$p \wedge q$
$\sim (p \wedge q)$
$\sim\left(p^{\wedge} q\right) \vee q$
$p \vee q$
$p \rightarrow(p \vee q)$
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
| $p$ | $q$ | $p \wedge q$ | $\sim (p \wedge q)$ | $\sim\left(p^{\wedge} q\right) \vee q$ | $p \vee q$ | $p \rightarrow(p \vee q)$ |
|---|---|---|---|---|---|---|
| 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 |