Step 1: Understanding the Question:
A tautology is a statement that is always true (T) for every possible combination of truth values of its components. Step 3: Detailed Explanation:
Let's analyze the options:
(A) $(\sim q \wedge p) \wedge (p \wedge \sim p)$: Since $(p \wedge \sim p)$ is always False (F), the entire conjunction is always False (Contradiction).
(B) $(p \wedge q) \wedge (\sim p \wedge q) \equiv (p \wedge \sim p) \wedge (q \wedge q) \equiv \text{F} \wedge q \equiv \text{F}$. (Contradiction).
(C) $[(\sim q) \wedge p] \wedge q \equiv (\sim q \wedge q) \wedge p \equiv \text{F} \wedge p \equiv \text{F}$. (Contradiction).
(D) $(\sim q \wedge p) \vee (p \vee \sim p)$: Since $(p \vee \sim p)$ is always True (T), any expression disjoined with True is always True.
$[ (\dots) \vee \text{T} ] \equiv \text{T}$. Step 4: Final Answer:
Option D is a tautology.