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 , whereas a theorem is believed to be true .

Answer 1

An axiom is a foundational statement assumed to be true without proof, while a theorem is a statement proven to be true through logical deductions.

Step-by-step explanation:

The difference between an axiom and a theorem lies in their respective roles within mathematics. An axiom is a foundational statement that is taken to be true without proof and serves as a starting point for further logical reasoning. It is an accepted premise of logic around which other statements are built. On the other hand, a theorem is a statement that has been proven to be true through a sequence of logical deductions, using axioms and previously established theorems.