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What is the difference between an axiom and a theorem?

An axiom is a statement believed to be true without requiring proof, whereas a theorem is believed to be based on logical deduction.

A. true
B. by observation
C. based on logical deduction
D. without requiring proof

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Final answer:

An axiom is an assumed true statement, while a theorem is derived through logical deduction from axioms or other theorems.


Explanation:

An axiom is a statement believed to be true without requiring proof.

A theorem, on the other hand, is a statement that is derived by logical deduction based on axioms or other theorems.

For example, in geometry, the statement 'The angles opposite the equal sides of an isosceles triangle are equal' is a theorem derived from the axioms of geometry.


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