Q. If $p \to (\sim p \vee \, \sim q)$ is false, then the truth values of p and q are respectively :
Solution:
$P \rightarrow \left(\sim P \vee\sim q\right)$
Now, make truth table of the given statement
p
q
$\sim p$
$\sim q$
$\sim p \vee \sim q$
$p \rightarrow(\sim p \vee \sim q)$
T
T
F
F
F
F
T
F
F
T
T
T
F
T
T
F
T
T
F
F
T
T
T
T
| p | q | $\sim p$ | $\sim q$ | $\sim p \vee \sim q$ | $p \rightarrow(\sim p \vee \sim q)$ |
|---|---|---|---|---|---|
| T | T | F | F | F | F |
| T | F | F | T | T | T |
| F | T | T | F | T | T |
| F | F | T | T | T | T |