The statement $$(p \Rightarrow q) \vee (p \Rightarrow r)$$ is NOT equivalent to:

We need to determine which statement is NOT equivalent to $$(p \Rightarrow q) \vee (p \Rightarrow r)$$.

We first simplify the given statement. We know $$p \Rightarrow q \equiv \sim p \vee q$$ and $$p \Rightarrow r \equiv \sim p \vee r$$. So $$(p \Rightarrow q) \vee (p \Rightarrow r) \equiv (\sim p \vee q) \vee (\sim p \vee r) \equiv \sim p \vee q \vee r$$. This is equivalent to $$p \Rightarrow (q \vee r)$$.

Now we check each option:

Option A: $$(p \wedge \sim r) \Rightarrow q \equiv \sim(p \wedge \sim r) \vee q \equiv \sim p \vee r \vee q$$. This equals $$\sim p \vee q \vee r$$. Equivalent.

Option B: $$\sim q \Rightarrow (\sim r \vee p) \equiv q \vee \sim r \vee p$$. This is $$p \vee q \vee \sim r$$, which is NOT the same as $$\sim p \vee q \vee r$$. For example, when $$p = T, q = F, r = T$$: our expression gives $$F \vee F \vee T = T$$, but Option B gives $$T \vee F \vee F = T$$. Try $$p = T, q = F, r = F$$: our expression gives $$F \vee F \vee F = F$$, but Option B gives $$T \vee F \vee T = T$$. So they differ. NOT equivalent.

Option C: $$p \Rightarrow (q \vee r) \equiv \sim p \vee q \vee r$$. Equivalent (same as our simplified form).

Option D: $$(p \wedge \sim q) \Rightarrow r \equiv \sim(p \wedge \sim q) \vee r \equiv \sim p \vee q \vee r$$. Equivalent.

Hence, the correct answer is Option B: $$\sim q \Rightarrow (\sim r \vee p)$$.