Given P->Q and Q->R, which statement is true: P -> R?

• A. R implies P
• B. P implies R
• C. Q implies P
• D. Cannot be determined

Answer: (B)

Chaining implications shows up often in logic: if P leads to Q and Q leads to R, then P leads to R. Think it through by assuming P is true. If P is true, Q must be true because P -> Q. If Q is true, R must be true because Q -> R. So whenever P is true, R is true, which is exactly what P -> R says. This holds regardless of whether P is actually true or false, since an implication with a false antecedent is true by default in standard logic. The other options aren’t guaranteed by the given premises—for example, R implies P would require R to force P, which isn’t established, and similarly Q implies P isn’t guaranteed. Therefore, the statement P implies R is the correct result of chaining the two implications.