Which is the reverse of a theorem?

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

Answer: (D)

The reverse of a theorem is its converse: you take a conditional statement that goes from one condition to a conclusion, and you swap them. So if a theorem says “If P then Q,” its converse says “If Q then P.” This is a separate statement and may be true or false independently of the original theorem; proving the theorem does not automatically prove the converse.

For example, a shape that is a square is a rectangle (true). The converse—if a shape is a rectangle, then it is a square—is not true in general.

Other terms differ in meaning: an axiom is a basic assumed truth used as a starting point; a corollary is a result that follows directly from the theorem; a proof is the logical argument that establishes the theorem. Hence the reverse of a theorem is specifically the converse.