Which term describes using previously proven results to deduce new statements?

• A. Corollary
• B. Imply
• C. Axiom
• D. Proof

Answer: (B)

Using proven results to deduce new statements is about implication. In logic, if a statement is known to be true (a proven fact), then another statement follows from it; we say the first statement implies the second. This is the way we extend established results to additional conclusions. A concrete example is: if a function is differentiable at a point, then it is continuous at that point. That shows how a proven property (differentiability) yields a new true statement (continuity) via implication.

The other terms have different roles: an axiom is an assumed starting truth with no proof; a proof is the justification that establishes a statement; a corollary is a result that follows directly from a proven theorem, usually named as a consequence rather than the general act of deducing from proven facts.