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Let's solve the truth table problem based on the logical formula \(\neg (q \lor p)\).

Here’s the breakdown for each combination of \( p \) and \( q \):

1. **\( p = T, q = T \)**:
   - \( q \lor p = T \lor T = T \)
   - \( \neg (q \lor p) = \neg T = F \)

2. **\( p = T, q = F \)**:
   - \( q \lor p = F \lor T = T \)
   - \( \neg (q \lor p) = \neg T = F \)

3. **\( p = F, q = T \)**:
   - \( q \lor p = T \lor F = T \)
   - \( \neg (q \lor p) = \neg T = F \)

4. **\( p = F, q = F \)**:
   - \( q \lor p = F \lor F = F \)
   - \( \neg (q \lor p) = \neg F = T \)

Thus, the completed truth table for \(\neg (q \lor p)\) is:

- \( F \) when \( p = T, q = T \)
- \( F \) when \( p = T, q = F \)
- \( F \) when \( p = F, q = T \)
- \( T \) when \( p = F, q = F \)

Would you like more details on this or do you have any other questions? Here are some related topics we could explore:

1. What would the truth table look like if we consider the formula \((p \land q)\)?
2. How does the truth table change if the operation is \(\neg q \land p\)?
3. Why is the negation of \( q \lor p \) the same as \(\neg q \land \neg p\) (De Morgan's Laws)?
4. Can you explain how to construct a truth table for the implication \( p \rightarrow q \)?
5. What is the significance of using logical operators in programming?

**Tip:** When working with truth tables, it's useful to start by calculating the simplest expressions first (like \( q \lor p \)) before moving on to more complex expressions (like \(\neg (q \lor p)\)). This step-by-step approach helps avoid mistakes.

Complete the following truth table for \( \neg (q \lor p) \), using T for true and F for false.

Solve the truth table for \( \neg (q \lor p) \). Learn how to calculate the values for each combination of p and q, applying negation and the disjunction (OR) operation. Suitable for high school students studying logic and truth tables.

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