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Mathematical Reasoning
medium
The Boolean expression $(p \wedge \sim q) \Rightarrow(q \vee \sim p)$ is equivalent to:
A
$\sim q \Rightarrow p$
B
$\mathrm{p} \Rightarrow \mathrm{q}$
C
$\mathrm{p} \Rightarrow \sim \mathrm{q}$
D
$\mathrm{q} \Rightarrow \mathrm{p}$
(JEE MAIN-2021)
Solution
| $p$ | $q$ | $\sim \mathrm{p}$ | $\sim \mathrm{q}$ | $\mathrm{p} \wedge \sim \mathrm{p}$ | $(\mathrm{p} \vee \sim \mathrm{q})$ | $(\mathrm{p} \wedge \sim \mathrm{p}) \Rightarrow(\mathrm{qv} \sim \mathrm{p})$ | $\mathrm{p} \Rightarrow \mathrm{q}$ |
| $T$ | $F$ | $F$ | $T$ | $T$ | $F$ | $F$ | $F$ |
| $F$ | $T$ | $T$ | $F$ | $F$ | $T$ | $T$ | $T$ |
| $T$ | $T$ | $F$ | $F$ | $F$ | $T$ | $T$ | $T$ |
| $F$ | $F$ | $T$ | $T$ | $F$ | $T$ | $T$ | $T$ |
$(\mathrm{P} \wedge \sim \mathrm{q})(\mathrm{q} \vee \sim \mathrm{p})$
$\equiv \mathrm{p} \Rightarrow \mathrm{q}$
Standard 11
Mathematics
