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

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Multiple Choice

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

To determine the truth value of the expression p ∧ q, it is important to understand how the logical conjunction (AND operator) functions. The p ∧ q expression is true only when both p and q are true. In this scenario, we are given that p is true and q is false. Thus, when we evaluate p ∧ q: - Since p is true and q is false, the conjunction of p and q becomes true AND false. - The result of true AND false is false because for the conjunction to be true, both parts must be true. Therefore, the truth value of p ∧ q is indeed false, confirming that the correct selection is the one that indicates that the expression evaluates to false.

To determine the truth value of the expression p ∧ q, it is important to understand how the logical conjunction (AND operator) functions. The p ∧ q expression is true only when both p and q are true.

In this scenario, we are given that p is true and q is false. Thus, when we evaluate p ∧ q:

  • Since p is true and q is false, the conjunction of p and q becomes true AND false.

  • The result of true AND false is false because for the conjunction to be true, both parts must be true.

Therefore, the truth value of p ∧ q is indeed false, confirming that the correct selection is the one that indicates that the expression evaluates to false.

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