The Boolean expression $$(p \wedge q) \Rightarrow ((r \wedge q) \wedge p)$$ is equivalent to:

We have to simplify the statement $$ (p \wedge q)\;\Rightarrow\;\bigl((r \wedge q)\;\wedge\;p\bigr)\;. $$

First recall the basic implication law:

$$A \Rightarrow B \;\equiv\; \neg A \,\vee\, B.$$

Before using the law, it is convenient to tidy up the right-hand conjunction. Because conjunction is both commutative and associative, we may rearrange the factors freely:

$$ (r \wedge q) \wedge p \;=\; p \wedge q \wedge r. $$

So the whole expression becomes

$$ (p \wedge q)\;\Rightarrow\;(p \wedge q \wedge r). $$

Now set $$A = (p \wedge q),\qquad B = (p \wedge q \wedge r).$$ Applying the implication law we obtain

$$ \neg(p \wedge q) \;\vee\; (p \wedge q \wedge r). $$

Next, use De Morgan’s rule for the negation of a conjunction:

$$ \neg(p \wedge q) \;=\; \neg p \;\vee\; \neg q. $$

Substituting this result we have

$$ (\neg p \;\vee\; \neg q) \;\vee\; (p \wedge q \wedge r). $$

The disjunction symbol “∨” is associative, so we can write the whole thing as

$$ \neg p \;\vee\; \neg q \;\vee\; (p \wedge q \wedge r). $$

To see the final simplification clearly, break the analysis into the two possible truth-values of $$q$$.

Case 1: $$q$$ is false. If $$q$$ is false, then $$\neg q$$ is true, and the entire disjunction is automatically true. Therefore the expression is true irrespective of $$p$$ and $$r$$.

Case 2: $$q$$ is true. If $$q$$ is true, the term $$\neg q$$ becomes false, and the disjunction reduces to

$$ \neg p \;\vee\; (p \wedge r). $$

Factor $$p$$ out of the second term:

$$ \neg p \;\vee\; \bigl(p \wedge r\bigr) \;=\; (\neg p \;\vee\; p) \wedge (\neg p \;\vee\; r) \;=\; \text{T} \wedge (\neg p \;\vee\; r) \;=\; \neg p \;\vee\; r. $$

Hence, when $$q$$ is true, the original statement is equivalent to $$\neg p \;\vee\; r$$. Remembering that $$q$$ itself is true in this case, $$\neg p \;\vee\; r \quad\equiv\quad \neg p \;\vee\; (r \wedge q).$$ (The factor $$q$$ can be inserted because $$q$$ is already true and $$r \wedge q$$ therefore has the same truth value as $$r$$.)

Combining both cases, we can write the simplified form valid for all truth-values of $$p,q,r$$ as

$$ \neg p \;\vee\; \neg q \;\vee\; (r \wedge q). $$

Finally recognise this again as an implication, with antecedent $$(p \wedge q)$$ and consequent $$(r \wedge q)$$:

$$ \neg(p \wedge q) \;\vee\; (r \wedge q) \;\equiv\; (p \wedge q) \Rightarrow (r \wedge q). $$

Thus the original Boolean expression is logically equivalent to $$ (p \wedge q) \Rightarrow (r \wedge q). $$

Comparing with the given options, this matches Option C.

Hence, the correct answer is Option C.