Question

select the correct answer from each drop - down menu. which are the best definitions for theorem, conjecture, and axiom? a statement that is assumed to be true without proof is a(n)
. a statement that has been shown to be true by vigorous application of logic is a(n)
. a(n)
is a statement that is believed to be true but hasnt been proven.

Explanation:

1. For the first blank (A statement that has been shown to be true by vigorous application of logic is a(n) $\boldsymbol{\text{theorem}}$): A theorem is a statement proven using logical reasoning and previously established facts.
2. For the second blank (A statement that is assumed to be true without proof is a(n) $\boldsymbol{\text{axiom}}$): An axiom (or postulate) is a fundamental statement accepted as true without requiring proof, serving as a starting point for reasoning.
3. For the third blank (A(n) $\boldsymbol{\text{conjecture}}$ is a statement that is believed to be true but hasn't been proven): A conjecture is a proposition that is suspected to be true based on evidence or intuition but lacks a formal proof.

Answer:

1. A statement that has been shown to be true by vigorous application of logic is a(n) $\boldsymbol{\text{theorem}}$.
2. A statement that is assumed to be true without proof is a(n) $\boldsymbol{\text{axiom}}$.
3. A(n) $\boldsymbol{\text{conjecture}}$ is a statement that is believed to be true but hasn't been proven.