Q. If the truth value of the Boolean expression $((p \vee q) \wedge(q \rightarrow r) \wedge(\sim r)) \rightarrow(p \wedge q)$ is false, then the truth values of the statements $p , q , r$ respectively can be:
Solution:
$p$
$q$
$r$
$\underbrace{p \vee q}_{a}$
$\underbrace{q \to r}_{b}$
$a \wedge b$
$\sim r$
$\underbrace{a \wedge b \wedge( \sim r)}_{c}$
$\underbrace{p \wedge q}_{d}$
$c \to d$
T
F
T
T
T
T
F
F
F
T
F
F
T
F
T
F
F
F
F
T
T
F
F
T
T
T
T
T
F
F
F
T
F
T
F
F
T
F
F
T
| $p$ | $q$ | $r$ | $\underbrace{p \vee q}_{a}$ | $\underbrace{q \to r}_{b}$ | $a \wedge b$ | $\sim r$ | $\underbrace{a \wedge b \wedge( \sim r)}_{c}$ | $\underbrace{p \wedge q}_{d}$ | $c \to d$ |
|---|---|---|---|---|---|---|---|---|---|
| T | F | T | T | T | T | F | F | F | T |
| F | F | T | F | T | F | F | F | F | T |
| T | F | F | T | T | T | T | T | F | F |
| F | T | F | T | F | F | T | F | F | T |