Final answer:
Conclusions are not building blocks of proofs but rather the results. Definitions, axioms, and logical reasoning are fundamental components of constructing formal and informal proofs in mathematics.
Step-by-step explanation:
The building blocks of an informal or formal proof in mathematics are definitions, axioms, and logical reasoning. Conclusions are the results of a proof, not the building blocks. Therefore, the correct answer to the student's question, which of the following are NOT building blocks of an informal or formal proof, is c. Conclusions.
Understanding Different Types of Reasoning
Inductive reasoning involves making a generalization based on specific observations, while deductive reasoning involves starting with a general statement and reaching a conclusion about a specific case. Critical thinking and logical reasoning serve as the backbone for constructing proofs and arguments. Without precise definitions and accepted axioms, which are fundamental truths in mathematics, a formal proof cannot be established. Meanwhile, logical reasoning allows for the proper connection between these elements, leading to valid conclusions.
Regarding the provided reference materials, deductive reasoning uses valid argument structures, such as Disjunctive Syllogism, to infer conclusions based on premises. Logic and mathematical rules ensure the structure of the argument leads to true conclusions, provided the premises themselves are true. If an argument guarantees the truth of its conclusion given its premises are true, then it is a valid deductive argument. This is a crucial concept within proofs in mathematics.