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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

Question

25-06-2024
Mathematics

Answered

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 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

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-06-25T11:35:53-04:00

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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