Mathematical prompt logic and reasoning examples illustrate the fundamental building blocks of mathematical reasoning, including variables, expressions, equations, and inequalities. They also encompass various reasoning skills such as deductive, inductive, and analogical reasoning, and highlight the process of constructing logical arguments and proofs. These prompts cover topics such as theorem proving, hypothesis testing, and conjecture exploration, demonstrating the rigorous and logical nature of mathematical reasoning and its applications in problem-solving and mathematical discovery.