The negation of p → ( ∼ p ∨ q ) is

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The negation of $p \rightarrow(\sim p \vee q)$ is

MathematicsMathematical ReasoningKCETKCET 2011

Options:

A $p \vee(p \vee \sim q)$
B $p \rightarrow \sim(p \vee q)$
C $p \rightarrow q$
D $p \wedge \sim q$

Solution:

2035 Upvotes Verified Answer

The correct answer is: $p \wedge \sim q$

Here, we observe that the truth value of column $\sim[p \rightarrow(\sim p \vee q)]$ and $(p \wedge \sim q)$ are same. Hence,
$$
-[p \rightarrow(-p \vee q)]=(p \wedge-q)
$$

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