Which expression represents the conjunction of P and Q?

Which expression represents the conjunction of P and Q?

• A. P and Q
• B. P or Q
• C. Q -> P
• D. Not P -> Q

Answer: (A)

Conjunction means both statements must be true at the same time. Saying “P and Q” asserts that P is true and Q is true, so the expression is true only when both P and Q are true. That exactly captures the idea of the conjunction of P and Q. The other forms represent different operations: “P and Q” is not the same as “P or Q,” which is true if either P or Q (or both) is true. An implication like “Q implies P” is true in all cases except when Q is true and P is false. “Not P implies Q” is another implication, which is not expressing a conjunction.

Conjunction means both statements must be true at the same time. Saying “P and Q” asserts that P is true and Q is true, so the expression is true only when both P and Q are true. That exactly captures the idea of the conjunction of P and Q.

The other forms represent different operations: “P and Q” is not the same as “P or Q,” which is true if either P or Q (or both) is true. An implication like “Q implies P” is true in all cases except when Q is true and P is false. “Not P implies Q” is another implication, which is not expressing a conjunction.