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The problem asks to find the truth value of the logical expression \( p \lor \neg q \) given that:

- \( p \) is true,
- \( q \) is false.

Let’s break down the expression:

1. **Negation of \( q \) (i.e., \( \neg q \))**: Since \( q \) is false, \( \neg q \) (not \( q \)) is true.
   
2. **Disjunction (OR) \( p \lor \neg q \)**: 
   - The logical OR (\( \lor \)) is true if at least one of the operands is true.
   - \( p \) is true, and \( \neg q \) is also true.
   - Since both \( p \) and \( \neg q \) are true, the entire expression \( p \lor \neg q \) is true.

### Final Answer: True

Would you like any further explanation or have additional questions?

Here are 5 related questions for further practice:
1. What is the truth value of \( p \land \neg q \) given the same conditions?
2. If both \( p \) and \( q \) are false, what is the truth value of \( p \lor q \)?
3. How does the truth table of a disjunction \( p \lor q \) look?
4. What is the truth value of \( \neg (p \land q) \) if \( p \) is true and \( q \) is false?
5. What is the difference between conjunction and disjunction in logic?

**Tip:** Always remember that in logical OR (\( \lor \)), if either value is true, the whole expression evaluates to true.

If p is true and q is false, find the truth value of p ∨ ¬q.

Learn how to find the truth value of p ∨ ¬q when p is true and q is false. This problem demonstrates key concepts in propositional logic, focusing on disjunction and negation. Suitable for Grades 10-12.

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