What is the transitive consequence of P implies Q and Q implies R?

• A. R implies P
• B. Q implies P
• C. P implies Q
• D. P implies R

Answer: (D)

The idea being tested is that implication is transitive: if P leads to Q and Q leads to R, then P must lead to R. Picture it as a chain of events: whenever P happens, Q happens; and whenever Q happens, R happens; so whenever P happens, R happens as well. In logical form, from P → Q and Q → R you can deduce P → R. A handy example: P = “it rains,” Q = “the streets are wet,” R = “I carry an umbrella.” If rain makes the streets wet and wet streets make me carry an umbrella, then rain implies I carry an umbrella. This is why the direct consequence is P implies R.