Final answer:
Reducibility can indeed be used to demonstrate that a language is undecidable by reducing a known undecidable language to it. This method follows from the principles of computational theory and shows that the new language must be as complex or undecidable as the original. Understanding and translating between universal statements and conditional statements is valuable in logic for identifying the necessary and sufficient conditions they imply.
Step-by-step explanation:
To address the question: Reducibility is indeed used to show the relationship between formal languages, and it is true that to show that a language is undecidable, one could reduce a known undecidable language to it. If such a reduction is possible and the known undecidable language is reducible to the language in question, then the new language must also be undecidable. This follows from the definition of reducibility in computational theory, where if problem A is reducible to problem B and A is known to be undecidable, then B is either undecidable or at least as hard as A.
When considering universal statements and their logical equivalences to conditionals, translating between these forms helps clarify the necessity and sufficiency of the logical relations they represent. For example, the universal statement 'All men are mortal' can be transformed into the conditional 'If someone is a man, then he is mortal', which helps us understand the necessary condition for mortality in this context. Furthermore, counterexamples are powerful tools to disprove universal affirmative statements since finding even a single case that contradicts the statement invalidates its universality.