How are axioms described in the material?

• A. self-evident truths
• B. a string of symbols which has an intrinsic meaning only in the context of all derivable formulas of an axiomatic system
• C. Theorems derived from proofs
• D. Observations of nature

Answer: (A)

Axioms are the starting points you accept as true without proof within the system. They’re treated as self-evident truths that don’t need demonstration, providing the foundation from which all other statements (theorems) are logically derived through rules of inference. This is why the material describes axioms as self-evident truths.

Think of geometry: you take certain basic statements as given—like through any two points there is a unique line—and then prove many other results from those starting points. The other ideas don’t fit because a string of symbols with meaning only in the broader derivation describes the formal language, not the act of assuming basic truths; theorems are what you prove, not what you start with; and observations of nature are empirical evidence, not foundational assumptions of a formal system.