Which term is a statement or conjecture that can be proven to be true based on postulates, definitions, or other proven theorems?

Which term is a statement or conjecture that can be proven to be true based on postulates, definitions, or other proven theorems?

• A. Axiom
• B. Theorem
• C. Conjecture
• D. Postulate

Answer: (B)

A statement that can be proven true using basic assumptions (postulates), definitions, and previously proven results is a theorem. Postulates and axioms are the starting points we take as true without proof, and definitions clarify what we’re talking about. From those, a theorem is a statement whose truth is established through a logical proof that follows from those foundations. A conjecture, by contrast, is a claim that might be true but hasn’t been proven yet, and an axiom or postulate is simply an assumption you accept without proof. For example, the result that the sum of the interior angles of a triangle is 180 degrees is a theorem because it can be proven from the basic geometric postulates.

A statement that can be proven true using basic assumptions (postulates), definitions, and previously proven results is a theorem. Postulates and axioms are the starting points we take as true without proof, and definitions clarify what we’re talking about. From those, a theorem is a statement whose truth is established through a logical proof that follows from those foundations. A conjecture, by contrast, is a claim that might be true but hasn’t been proven yet, and an axiom or postulate is simply an assumption you accept without proof. For example, the result that the sum of the interior angles of a triangle is 180 degrees is a theorem because it can be proven from the basic geometric postulates.