What is the reverse of a theorem?

• A. Corollary
• B. Theorem
• C. Axiom
• D. Converse of a theorem

Answer: (D)

The concept being tested is what we call the converse of a theorem. A theorem is a statement of the form “If P then Q” that has been proven. The reverse is created by swapping the parts, giving “If Q then P.” The term for that swapped version is the converse of the theorem. For example, if we have “If a number is even, then its square is even,” the reverse would be “If a number’s square is even, then the number is even.” The converse isn’t automatically true just because the original theorem is true, though in some cases it is. The other options fit different ideas: a corollary is a result that follows easily from a theorem, an axiom is a basic assumed truth, and a theorem is the proven statement itself.