Q. The negation of $ \sim s \, \vee ( \sim \, r \wedge \, s)$ is equivalent to
Solution:
$\sim S V(\sim r \wedge S)$
S
r
$\sim r$
$\sim r \wedge S$
$\sim S$
$\sim S V(\sim r \wedge S)$
$\sim(\sim S V(\sim r \wedge S))$
T
T
F
F
F
F
T
T
F
T
T
F
T
F
F
T
F
F
T
T
F
F
F
T
F
T
T
F
| S | r | $\sim r$ | $\sim r \wedge S$ | $\sim S$ | $\sim S V(\sim r \wedge S)$ | $\sim(\sim S V(\sim r \wedge S))$ |
|---|---|---|---|---|---|---|
| T | T | F | F | F | F | T |
| T | F | T | T | F | T | F |
| F | T | F | F | T | T | F |
| F | F | T | F | T | T | F |