The compound statement $(\sim( P \wedge Q )) \vee((\sim P ) \wedge Q ) \Rightarrow((\sim P ) \wedge(\sim Q ))$ is equivalent to
The compound statement $(\sim( P \wedge Q )) \vee((\sim P ) \wedge Q ) \Rightarrow((\sim P ) \wedge(\sim Q ))$ is equivalent to
- [JEE MAIN 2023]
- A
$((\sim P ) \vee Q ) \wedge((\sim Q ) \vee P )$
- B
$(\sim Q) \vee P$
- C
$((\sim P ) \vee Q ) \wedge(\sim Q )$
- D
$(\sim P ) \vee Q$
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- [AIEEE 2009]
If the truth value of the Boolean expression $((\mathrm{p} \vee \mathrm{q}) \wedge(\mathrm{q} \rightarrow \mathrm{r}) \wedge(\sim \mathrm{r})) \rightarrow(\mathrm{p} \wedge \mathrm{q}) \quad$ is false then the truth values of the statements $\mathrm{p}, \mathrm{q}, \mathrm{r}$ respectively can be:
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- [JEE MAIN 2021]