In the Transylvania puzzle, half of the inhabitants are insane, and believe only false things, whereas the other half are sane and believe only true things. In addition, humans always tell the truth, and vampires always lie. Which of the follwing can be deduced from above statements??

In this logical system, sane humans always tell the truth (sane + believes true things), and insane vampires always lie but believe false things (insane + believes false things + vampire nature means lying). Therefore, statements from sane humans (truth about truth) or insane vampires (lying about falsehood) always result in true statements. The other combinations can produce false outputs.