Mathematical logic.
no
Postulates Definitions Corollaries
Yes, of course.
theoremPostulates(apex)postulatesdefinitioncollaries
Logically invalid statements.
No
no
Postulates Definitions Corollaries
Yes, of course.
conclusion
theoremPostulates(apex)postulatesdefinitioncollaries
Theorems, definitions, corollaries, and postulates
Logically invalid statements.
In a proof, statements that are purely opinion-based or subjective, such as personal beliefs or interpretations, cannot be used to justify steps. Additionally, unsupported assertions that lack logical reasoning or empirical evidence, as well as circular reasoning where the conclusion is included in one of the premises, are also invalid. Lastly, statements that are not universally accepted or established laws, such as conjectures that have not been proven, cannot justify proof steps.
Yes, a postulate can be used to explain the steps of a proof as it provides foundational assumptions that are accepted without proof. In a proof, postulates serve as starting points or premises from which logical deductions can be made. By referencing postulates, one can justify certain steps in the proof, helping to establish the validity of the overall argument. This creates a structured framework for demonstrating theorems or propositions.
Since you didn't include the statements in your question there is no way for us to know
Guess Conjecture