Is the argument form 'If P → Q; Q; Therefore P' valid?

• A. Sometimes.
• B. Only if Q is true.
• C. Yes.
• D. No.

Answer: (D)

The main idea tested is whether you can infer the original condition from a conditional claim and its consequent. From “If P then Q” together with Q being true, you cannot in general conclude P. This is a fallacy known as affirming the consequent: a true conditional and a true result do not necessarily mean the starting condition was true.

A concrete way to see this is to assign everyday truths: If you win the lottery, you are likely to be smiling. Suppose you are smiling. That doesn’t prove you won the lottery—you could be smiling for many other reasons. In this setup, the premises can all be true while P is false, so the conclusion doesn’t logically follow.

Only if P and Q were actually equivalent—meaning Q would force P as well—would the argument be valid. But that additional requirement isn’t provided here. Hence the form is not valid.