If p*p* is true and q*q* is false, find the truth value of:

\neg, p, or, \neg, q

¬*p*∨¬*q*

Given that \( p \) is true and \( q \) is false, let's evaluate the expression \( \neg p \lor \neg q \).

### Step 1: Identify the truth values
- \( p = \text{true} \)
- \( q = \text{false} \)

### Step 2: Determine the truth values of \( \neg p \) and \( \neg q \)
- \( \neg p \) is the negation of \( p \).
  - Since \( p = \text{true} \), \( \neg p = \text{false} \).
- \( \neg q \) is the negation of \( q \).
  - Since \( q = \text{false} \), \( \neg q = \text{true} \).

### Step 3: Evaluate \( \neg p \lor \neg q \)
- \( \neg p \lor \neg q \) is the logical "or" of \( \neg p \) and \( \neg q \).
- The "or" (\( \lor \)) operation is true if at least one of the operands is true.

In this case:
- \( \neg p = \text{false} \)
- \( \neg q = \text{true} \)

Since one of the operands is true, \( \neg p \lor \neg q \) is **true**.

### Final Answer:
The truth value of \( \neg p \lor \neg q \) is **true**.

Would you like more details or have any questions about this? 

Here are some related questions to explore:
1. What is the truth table for the disjunction (\( \lor \)) operation?
2. How does the truth value change if both \( p \) and \( q \) are true?
3. What is the truth value of \( \neg (p \lor q) \) given \( p = \text{true} \) and \( q = \text{false} \)?
4. How do logical operators like \( \lor \) and \( \neg \) apply in real-world scenarios?
5. What happens if both \( p \) and \( q \) are false in the expression \( \neg p \lor \neg q \)?

**Tip:** Understanding De Morgan's laws can be very helpful when dealing with negations and logical operators.

Explore how to evaluate the truth value of \( \neg p \lor \neg q \), given specific truth values for \( p \) and \( q \). Understand the application of logical negation and disjunction using detailed step-by-step solutions. Suitable for Grades 9-12.

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