Final answer:
The correct answer to what the law of noncontradiction states is option b) True contradictions don't admit a proof, as the law indicates that contradictory propositions cannot both be true.
Step-by-step explanation:
The law of noncontradiction is a fundamental principle in logic and philosophy which states that contradictory propositions cannot both be true. This principle underpins rational discourse and is essential to the structure of logical argumentation. According to Aristotle, who is a significant figure in establishing this law, a true statement is one that aligns with the reality it describes (e.g., 'A is B' is true if and only if A is indeed B). Further exploring this concept, the law of the excluded middle complements the law of noncontradiction by asserting that for any given statement, either the statement is true, or its negation is true.
Navigating the options presented in the student's question: a) True contradictions admit a proof, b) True contradictions don't admit a proof, c) All contradictions are provable, and d) Contradictions are necessarily provable, the principle that adheres to the law of noncontradiction is option b) True contradictions don't admit a proof. This is because, by definition, a true contradiction cannot exist, hence it is not provable.