Final answer:
The purpose of statements and reasons in a formal proof is to provide a logical structure composed of premises that support a conclusion, ensuring the proof's validity and credibility.
Step-by-step explanation:
The purpose of statements and reasons in a formal proof is to provide evidence and support for mathematical claims (Option a). This formal approach ensures that every step in the proof is justified, making the conclusion credible and trustworthy. In a logical framework, an argument is formed of premises that lead to a conclusion through a reasoning process called inference. The premises are the evidence that, when evaluated against formal logical standards, either support or do not support the conclusion.
Philosophers and mathematicians use logic to assess the validity of these proofs, distinguishing between the truth of the premises and the logical structure of the argument. This critical approach ensures coherence and credibility, leading to well-founded beliefs and explanations for observed phenomena. Logical statements may require conditional or universal affirmations that must stand up to counterexamples to establish their validity.