Question

Let \( p \) and \( q \) be two statements. Then, \( p \vee q \) is false if:

• A. \( p \) is false and \( q \) is true
• B. both \( p \) and \( q \) are false
• C. both \( p \) and \( q \) are true
• D. None of the above

Hint:

In logical operations, \( p \vee q \) (OR) is false only when both \( p \) and \( q \) are false.

Answer 1

The Correct Option is B

Step 1: Analyze the logical operation.
For the logical OR operation \( p \vee q \), it is false when both \( p \) and \( q \) are false.
Step 2: Conclusion.
Thus, \( p \vee q \) is false when both \( p \) and \( q \) are false.
Final Answer: \[ \boxed{both \, p \, and \, q \, are \, false} \]