Which of the following Boolean expressions is not a tautology?

We need to identify which Boolean expression is NOT a tautology. Recall that $$p \Rightarrow q \equiv \sim p \vee q$$.

Option A: $$(p \Rightarrow q) \vee (\sim q \Rightarrow p) \equiv (\sim p \vee q) \vee (q \vee p) \equiv (\sim p \vee p) \vee q \equiv T \vee q \equiv T$$. This is a tautology.

Option B: $$(q \Rightarrow p) \vee (\sim q \Rightarrow p) \equiv (\sim q \vee p) \vee (q \vee p) \equiv (\sim q \vee q) \vee p \equiv T \vee p \equiv T$$. This is a tautology.

Option C: $$(p \Rightarrow \sim q) \vee (\sim q \Rightarrow p) \equiv (\sim p \vee \sim q) \vee (q \vee p) \equiv (\sim p \vee p) \vee (\sim q \vee q) \equiv T \vee T \equiv T$$. This is a tautology.

Option D: $$(\sim p \Rightarrow q) \vee (\sim q \Rightarrow p) \equiv (p \vee q) \vee (q \vee p) \equiv p \vee q$$. When $$p = F$$ and $$q = F$$, this equals $$F$$. So this is NOT a tautology.

The answer is Option D.