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Mathematical Reasoning
medium
इनमें से कौन सा बूलीय व्यंजक $p \wedge \sim q$ के तुल्य है ?
A
$\sim(\mathrm{q} \rightarrow \mathrm{p})$
B
$\sim \mathrm{p} \rightarrow \sim \mathrm{q}$
C
$\sim(\mathrm{p} \rightarrow \sim \mathrm{q})$
D
$\sim(p \rightarrow q)$
(JEE MAIN-2021)
Solution
| $p$ | $q$ | $\sim \mathrm{p}$ | $\sim \mathrm{q}$ | $\mathrm{p}-\mathrm{q}$ | $\sim(\mathrm{p} \rightarrow \mathrm{q})$ | $\mathrm{q} \rightarrow \mathrm{p}$ | $\sim(\mathrm{q} \rightarrow \mathrm{p})$ |
| $T$ | $T$ | $F$ | $F$ | $T$ | $F$ | $T$ | $F$ |
| $T$ | $F$ | $F$ | $T$ | $F$ | $T$ | $T$ | $F$ |
| $F$ | $T$ | $T$ | $F$ | $T$ | $F$ | $F$ | $T$ |
| $F$ | $F$ | $T$ | $T$ | $T$ | $F$ | $T$ |
$F$ |
| $\mathrm{p} \wedge \sim \mathrm{q}$ | $\sim \mathrm{p} \rightarrow \sim \mathrm{q}$ | $\mathrm{p} \rightarrow \sim \mathrm{q}$ | $\sim(\mathrm{p} \rightarrow \sim \mathrm{q})$ |
| $F$ | $T$ | $F$ | $T$ |
| $T$ | $T$ | $T$ | $F$ |
| $F$ | $F$ | $T$ | $F$ |
| $F$ | $T$ | $T$ | $F$ |
$\mathrm{p} \wedge \sim \mathrm{q} \equiv \sim(\mathrm{p} \rightarrow \mathrm{q})$
Standard 11
Mathematics
