Which form of argument infers that if a conditional premise is true and the consequent is false, then the premise is false?

• A. Modus tollens
• B. Modus ponens
• C. Hypothetical syllogism
• D. Affirming the consequent

Answer: (A)

This is the rule known as denying the consequent (modus tollens). It says that if a conditional statement P -> Q is true and Q is false, then P must be false. In other words, a true if-then claim together with a failed result lets you deny the initial condition.

Think of it like: If it is raining, the ground is wet. The ground is not wet. Therefore, it is not raining. The truth of the conditional combined with the false outcome forces the negation of the condition that would have produced that outcome.

This differs from the other forms. Modus ponens would derive Q from P and P -> Q, not negate P. Hypothetical syllogism links two conditionals to form a new conditional, not a negation. Affirming the consequent would wrongly conclude P from Q and P -> Q, which is a fallacy.