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Mathematics
The negation of the compound proposition p∨ (.∼ p∨ q.) is
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Q. The negation of the compound proposition $p\lor \left(\right.\sim p\lor q\left.\right)$ is
NTA Abhyas
NTA Abhyas 2022
A
$\left(p \land \sim q\right)\land \sim p$
B
$\left(\right.p\land \sim q\left.\right)\lor \sim p$
C
$\left(\right.p\lor \sim q\left.\right)\lor \sim p$
D
None of these
Solution:
From the De Morgan's Law, $\sim \left(p \lor q\right)=\sim p\land \sim q$
So, the negation of $p\lor \left(\right.\sim p\lor q\left.\right)$
$\sim \left[\right.p\lor \left(\right.\sim p\lor q\left.\right)\left]\right.$
$=\sim p\land \sim \left(\right.\sim p\lor q\left.\right)$
$=\sim p\land \left(\right.p\land \sim q\left.\right)$