To solve this problem, let's evaluate each of the given logical expressions with the values provided: $p = F$, $q = T$, and $r = T$.

1. Option A: $q \lor r$

   • $q \lor r = T \lor T = T$
   • This expression evaluates to true.

2. Option B: $q \land r$

   • $q \land r = T \land T = T$
   • This expression evaluates to true.

3. Option C: $p \lor r$

   • $p \lor r = F \lor T = T$
   • This expression evaluates to true.

4. Option D: $\neg q$

   • $\neg q = \neg T = F$
   • This expression evaluates to false.

So, the expression that evaluates to false is Option D: $\neg q$.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. What are the truth tables for basic logical operations (AND, OR, NOT)?
2. How do you evaluate a compound logical expression?
3. What are De Morgan's laws in logic?
4. How do you convert a logical expression to its disjunctive normal form (DNF)?
5. How do logical gates in digital circuits relate to these expressions?

Tip: When dealing with logical expressions, always remember the truth tables for AND ($\land$), OR ($\lor$), and NOT ($\neg$) operations, as they are fundamental in evaluating the expressions.