D.1. Truth: The truth of a proposition belongs only to itself, and itself alone.
E.1. For identifying errors in reasoning, since we are dealing with the truth of a previously not known proposition, it raises the question: How does the truth of one proposition relate with another? And here is the central observation for all logical work:
The truth of something is only its truth, and not of anything else.
The truth of any proposition belongs only to itself implies that if something is true, all that defines it is also true and also its assumed consequent is true. Conversely, if it is false, at least one key component that defines it is false, or its assumed antecedent is false.
For an example consider if it is defined that rain is composed of water, and nothing else, and if is it believed that presence of rain implies presence of clouds, and we are informed that in such and such region it is raining, we may deduce that by definition there are additional, visually visible, water drops in air, an increased amount of water in air compared to case of no rain, and also that there are clouds. However, if we learn that there are no clouds in that region, we may deduce that there is no rain, and that the additional, visually visible, water drops in air are absent.
Contrasting to it now consider that I say, I ate an apple therefore aliens landed on Mars. Now the act of eating an apple neither defines anything related to aliens, nor its assumed consequents relate to Mars. Eating an apple has a consequent of gratifying hunger, and an antecedent of need of food, and it, by definition, is a processes of chewing something, and not of landing anywhere.
Thus, the truth of anything only establishes the truth of the components that define it, and of its assumed consequent. The falsehood of anything only establishes falsehood of at least one key component of definition, or falsehood of antecedents. The truth of anything does not establish the truth of an irrelevant. All that is neither part of definition, nor assumed consequent is irrelevant, and the only relevant is either part of definition or assumed consequent.
Reference: Copi, I., Cohen, C., & Rodych, V. (__). Introduction to logic. Routledge.