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

We have to simplify the Boolean expression $$ (p \Rightarrow q)\;\wedge\; (q \Rightarrow \sim p)\,. $$

First, recall the standard logical equivalence for an implication. The implication formula states:

$$ a \Rightarrow b \;\equiv\; \sim a \,\vee\, b. $$

Applying this to each implication in our expression, we replace the arrows by disjunctions:

For the first part, $$p \Rightarrow q \equiv \sim p \vee q.$$

For the second part, $$q \Rightarrow \sim p \equiv \sim q \vee \sim p.$$

Substituting these two results back into the original conjunction, we obtain

$$ (\sim p \vee q)\;\wedge\;(\sim q \vee \sim p). $$

Now we notice that both disjunctions contain the common literal $$\sim p.$$ To combine the two clauses, we use the distributive law of Boolean algebra, which says

$$ (A \vee B)\;\wedge\;(A \vee C)\;=\;A \;\vee\;(B \wedge C). $$

Here, we match the symbols as follows:

$$A = \sim p,\quad B = q,\quad C = \sim q.$$

Substituting into the distributive formula, we get

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

The expression $$q \wedge \sim q$$ is always false, because a statement and its negation can never be true at the same time. Hence

$$ q \wedge \sim q = \text{False}. $$

Therefore, our entire expression simplifies to

$$ \sim p \;\vee\; \text{False} \;=\; \sim p. $$

So the Boolean expression $$ (p \Rightarrow q) \wedge (q \Rightarrow \sim p) $$ is logically equivalent to $$\sim p.$$

Looking at the given options, $$\sim p$$ appears as Option D.

Hence, the correct answer is Option D.