If p is true and q is false, what is the truth value of p ∧ q?

The symbol \( p \wedge q \) represents the logical conjunction (AND) of \( p \) and \( q \). For a conjunction to be true, both \( p \) and \( q \) must be true. 

In this case:
- \( p \) is true
- \( q \) is false

Since \( q \) is false, the conjunction \( p \wedge q \) is **false**.

Would you like more details or have any other questions?

Here are 5 related questions:
1. What is the truth value of \( p \vee q \) (OR) if \( p \) is true and \( q \) is false?
2. What is the truth value of \( p \Rightarrow q \) (implication) when \( p \) is true and \( q \) is false?
3. How does the truth table for conjunction \( p \wedge q \) look like?
4. What happens if both \( p \) and \( q \) are false in a conjunction?
5. How is logical equivalence defined in truth tables?

**Tip:** In logical operations, conjunction (AND) is only true when all involved statements are true.

Understand the truth value of the logical conjunction p ∧ q when p is true and q is false. This problem explores key concepts in propositional logic, including the conjunction formula and truth table analysis. Suitable for students in Grades 9-12.

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