In the scenario where p is false and q is false, what is the outcome of p ∧ q?

In the scenario where p is false and q is false, what is the outcome of p ∧ q?

• A. True
• B. False
• C. Cannot be determined
• D. Both true

Answer: (B)

In logic, the conjunction operator ∧ (AND) combines two statements. For the expression p ∧ q to be true, both p and q must be true. In the scenario provided, both p and q are false. When evaluating p ∧ q: - Since p is false, it contributes a false value to the conjunction. - Since q is also false, it likewise adds a false value. The conjunction p ∧ q, therefore, results in a false outcome because both components need to be true for the entire expression to be true. If either or both components are false, the entire conjunction is false. Thus, the result of p ∧ q in this scenario is indeed false.

In logic, the conjunction operator ∧ (AND) combines two statements. For the expression p ∧ q to be true, both p and q must be true. In the scenario provided, both p and q are false.

When evaluating p ∧ q:

• Since p is false, it contributes a false value to the conjunction.

• Since q is also false, it likewise adds a false value.

The conjunction p ∧ q, therefore, results in a false outcome because both components need to be true for the entire expression to be true. If either or both components are false, the entire conjunction is false. Thus, the result of p ∧ q in this scenario is indeed false.