Question

Which of the following needs a proof?
$
  {\text{A}}{\text{. Theorem}} \\
  {\text{B}}{\text{. Axiom}} \\
  {\text{C}}{\text{. Definition}} \\
  {\text{D}}{\text{. Postulate}} \\
$

Answer 1

Hint: To determine the answer we read the definitions of each of the options and verify if they come under the category of needing a proof.

Complete step-by-step answer:

A Theorem is a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths.
An axiom is a statement or proposition which is regarded as being established, accepted, or self-evidently true.
A definition is a statement of the meaning of a term.
A postulate suggests or assumes the existence, fact, or truth of (something) as a basis for reasoning, discussion, or belief.
Axiom, Postulate and definition are self-evident & do not need any proof. Theorem is a proposition which needs a proof to establish its truth.
Therefore, the theorem needs a proof.
Hence, option A is correct.

Note: In order to solve questions of this type the key is to understand the definition of a proof, and the others given in the options and then figure out what fits into the category of needing a proof. That way we determine the answer.