Question

The negation of the compound proposition $p \vee (\neg p \vee q)$ is

• A. $(p \wedge \neg q) \wedge \neg p$
• B. $(p \wedge \neg q) \vee \neg p$
• C. $(p \wedge \neg q) \vee \neg p$
• D. None of the above

Hint:

Always simplify compound propositions first. $p \vee \neg p \equiv \mathbf{T}$ (tautology) and $\neg \mathbf{T} \equiv \mathbf{F}$ (contradiction).

Answer 1

The Correct Option is D

Step 1: Conceptual Understanding:
Simplify the proposition using logical equivalences before negating.
Step 2: Explanation in Detail:
$p \vee (\neg p \vee q) \equiv (p \vee \neg p) \vee q \equiv \mathbf{T} \vee q \equiv \mathbf{T}$.
The negation of a tautology is a contradiction $\mathbf{F}$, which is not listed among the options.
Step 3: Therefore, Stating the Final Answer
The negation is $\mathbf{F}$ (always false), so the answer is (D) None of the above.