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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.

Select the expression that evaluates to false. Given: p = F, q = T, r = T.

Learn how to evaluate logical expressions using Boolean variables (p = F, q = T, r = T). This problem covers the truth table for AND, OR, and NOT operations, suitable for students in Grades 9-12.

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