Question

1. which is the best definition of mathematical proof?

statements that show the assertion is false using a counterexample.
a sequence of statements that demonstrates the truth of an assertion.
a paragraph that always has three parts and shows that an assertion is true.
statements in any order that show that an assertion is true.

Explanation:

• The first option describes disproving an assertion with a counterexample, not a proof.
• The third option is incorrect because proofs do not require a fixed three-part paragraph structure.
• The fourth option is wrong because proofs rely on a logical, ordered sequence of statements, not random order.
• The second option correctly defines a mathematical proof as a logical sequence of statements that confirms an assertion is true.

Answer:

A sequence of statements that demonstrates the truth of an assertion.