The negation of the compound proposition $p \vee (\neg p \vee q)$ is
Show Hint
- $(p \wedge \neg q) \wedge \neg p$
- $(p \wedge \neg q) \vee \neg p$
- $(p \wedge \neg q) \vee \neg p$
- None of the above
The Correct Option is D
Solution and Explanation
Simplify the proposition using logical equivalences before negating.
Step 2: Detailed Explanation:
$p \vee (\neg p \vee q) \equiv (p \vee \neg p) \vee q \equiv \mathbf{T} \vee q \equiv \mathbf{T}$.
The negation of a tautology is a contradiction $\mathbf{F}$, which is not listed among the options.
Step 3: Final Answer:
The negation is $\mathbf{F}$ (always false), so the answer is (D) None of the above.
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