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Mathematical Reasoning
easy
The compound statement $(\mathrm{P} \vee \mathrm{Q}) \wedge(\sim \mathrm{P}) \Rightarrow \mathrm{Q}$ is equivalent to:
A
$P \vee Q$
B
$\sim(P \Rightarrow Q) \Leftrightarrow P \wedge \sim Q$
C
$P \wedge \sim Q$
D
$\sim(P \Rightarrow Q)$
(JEE MAIN-2021)
Solution
Using Truth Table
| $\mathrm{P}$ | $\mathrm{Q}$ | $\mathrm{P} \vee \mathrm{Q}$ | $\sim \mathrm{P}$ | $(\mathrm{P} \vee \mathrm{Q}) \wedge \mathrm{P}$ | $(\mathrm{P} \vee \mathrm{Q}) \wedge \sim \mathrm{P} \rightarrow \mathrm{Q}$ |
| $T$ | $T$ | $T$ | $F$ | $F$ | $T$ |
| $T$ | $F$ | $T$ | $F$ | $F$ | $T$ |
| $F$ | $T$ | $T$ | $F$ | $T$ | $T$ |
| $F$ | $F$ | $F$ | $T$ | $F$ | $T$ |
Check from options
Standard 11
Mathematics
