What is the term for a series of logical steps used to prove a theorem?

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Multiple Choice

What is the term for a series of logical steps used to prove a theorem?

Explanation:
A proof is a sequence of logical steps that shows a theorem is true beyond doubt. It starts from accepted starting points—axioms, definitions, and previously established results—and uses valid reasoning to deduce the statement. A proof must be rigorous and complete, with each step justified, so there are no gaps. Think of the other terms as different roles: an axiom is a basic assumption we accept without proof; a corollary is a result that follows directly from a proven theorem; the converse is the reverse implication of a statement, which is not automatically true and isn’t the process of proving the original theorem. For example, to prove that the sum of two even numbers is even, you express each even number as 2k and 2m, add them to get 2(k + m), which is again of the form 2 times an integer, hence even. This illustrates how a proof establishes truth through a clear chain of reasoning.

A proof is a sequence of logical steps that shows a theorem is true beyond doubt. It starts from accepted starting points—axioms, definitions, and previously established results—and uses valid reasoning to deduce the statement. A proof must be rigorous and complete, with each step justified, so there are no gaps.

Think of the other terms as different roles: an axiom is a basic assumption we accept without proof; a corollary is a result that follows directly from a proven theorem; the converse is the reverse implication of a statement, which is not automatically true and isn’t the process of proving the original theorem. For example, to prove that the sum of two even numbers is even, you express each even number as 2k and 2m, add them to get 2(k + m), which is again of the form 2 times an integer, hence even. This illustrates how a proof establishes truth through a clear chain of reasoning.

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