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Which are the best definitions for theorem, conjecture, and axiom?

1. A statement that is assumed to be true without proof is a(n) .
2. A statement that has been shown to be true by rigorous application of logic is a(n) .
3. A statement that is believed to be true but hasn't been proven is a(n) .

A. Theorem
B. Conjecture
C. Axiom

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Axioms serve as the foundation of deductive systems like geometry, theorems build upon initial assumptions, and geometry offers practical utility despite lacking experimental refutation.

Explanation:

Axioms are the starting assumptions in deductive systems, such as geometry, and are not proven but assumed to be true to prove other statements.

Theorems in geometry are logical deductions derived from original definitions and assumptions, building upon simpler results to deduce more complex ones.

While Geometry may not rely on experimental refutation like some sciences, its propositions can still provide valuable insights and practical applications in fields like engineering.

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