If P implies Q and Q implies R, which deduction must be true?

If P implies Q and Q implies R, which deduction must be true?

• A. P implies R
• B. Q implies P
• C. R implies Q
• D. P and Q are independent

Answer: (A)

Transitivity of implication is being tested here: if one statement implies a second, and that second implies a third, then the first must imply the third as well. So, if P implies Q and Q implies R, it follows that P implies R. The reasoning is straightforward: whenever P is true, Q must be true; and whenever Q is true, R must be true; therefore, whenever P is true, R must be true. This is the deduction that must hold regardless of how P, Q, or R are actually in the world. The other ideas aren’t guaranteed by the given information: the reverse implications (Q implies P, or R implies Q) aren’t specified, and saying P and Q are independent contradicts the first implication.

Transitivity of implication is being tested here: if one statement implies a second, and that second implies a third, then the first must imply the third as well. So, if P implies Q and Q implies R, it follows that P implies R. The reasoning is straightforward: whenever P is true, Q must be true; and whenever Q is true, R must be true; therefore, whenever P is true, R must be true.

This is the deduction that must hold regardless of how P, Q, or R are actually in the world. The other ideas aren’t guaranteed by the given information: the reverse implications (Q implies P, or R implies Q) aren’t specified, and saying P and Q are independent contradicts the first implication.