Question

select the correct answer from each drop - down menu. what is the difference between an axiom and a theorem? an axiom is a statement believed to be true
without requiring proof
, whereas a theorem is believed to be true

reset

Explanation:

To determine the difference between an axiom and a theorem, we recall their definitions. An axiom is a statement accepted as true without proof (it's a fundamental assumption). A theorem is a statement that is proven to be true based on previously established statements (like axioms, postulates, or other theorems) through logical deduction. So the second blank should be filled with "based on logical deduction" as theorems are derived via logical reasoning from other true statements.

Answer:

An axiom is a statement believed to be true \(\boldsymbol{\text{without requiring proof}}\), whereas a theorem is believed to be true \(\boldsymbol{\text{based on logical deduction}}\).