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
drop - down menu with options: based on logical deduction, within defined parameters, without requiring proof
, whereas a theorem is believed to be

Explanation:

To determine the correct option for the first blank (describing an axiom), we recall the definitions: an axiom is a statement accepted as true without needing a proof. The option "without requiring proof" matches this definition. For the second part (describing a theorem), a theorem is a statement proven true based on logical deduction (using axioms, postulates, etc.). So the first blank should be "without requiring proof" and the second (for the theorem) would be "based on logical deduction", but focusing on the first drop - down here, the correct option for the axiom's description is "without requiring proof".

Answer:

without requiring proof