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At Johnmiedema.ca, we're here to help you find answers. No question is unanswerable here.

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 rigorous application of logic is a(n) ______.

- A statement that is believed to be true but hasn't been proven is a(n) ______.

Axioms are assumed true, theorems are proven true, and conjectures are believed true but unproven.

**Axiom:** A statement that is assumed to be true without proof.

**Theorem:** A statement that has been shown to be true by vigorous application of logic.

**Conjecture:** A statement that is believed to be true but hasn't been proven yet.