If p and q are false, what is the truth value of ¬ (p Λ q)?

To determine the truth value of the expression \( \neg (p \land q) \), we need to follow these steps:

1. **Understand the components**:
   - \( p \) and \( q \) are both false (\( F \)).
   - \( \land \) is the logical "and" operator, which results in true only if both operands are true.
   - \( \neg \) is the logical "not" operator, which inverts the truth value.

2. **Evaluate the expression inside the parentheses**:  
   \( p \land q \)  
   Since both \( p \) and \( q \) are false, \( p \land q \) is also false.

   \[
   p \land q = F \land F = F
   \]

3. **Apply the negation**:
   \[
   \neg (p \land q) = \neg F = T
   \]

Thus, the truth value of \( \neg (p \land q) \) is **true**.

Would you like more details, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. What is the truth value of \( p \lor q \) when both \( p \) and \( q \) are false?
2. How does the truth table of \( \neg (p \lor q) \) compare with \( \neg (p) \land \neg (q) \)?
3. What is the truth value of \( \neg (p \lor q) \) if \( p \) is true and \( q \) is false?
4. Can you explain De Morgan's laws using the given expression?
5. What happens to the truth value of \( \neg (p \land q) \) if \( p \) is true and \( q \) is false?

**Tip**: When working with logical expressions, it's helpful to construct truth tables to visualize how different operators affect the truth values.

Discover how to evaluate the truth value of the logical expression ¬(p Λ q) when both p and q are false. This problem explores key concepts in propositional logic and applies fundamental logical operators. Suitable for students in Grades 9-12.

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