5.2. Three students, Anna, Vika, and Masha, study at the Literature, History, and Biology faculties. If Anna is a literature student, then Masha is not a historian. If Vika is not a historian, then Anna is a literature student. If Masha is not a literature student, then Vika is a biologist. Which girl studies at which faculty?
Answer: Vika is a historian, Anna is a biologist, Masha is a philologist.

Solution. Suppose Vika is not a historian, then (by condition 2) Anna is a philologist, but if Anna is a philologist, then Masha is not a historian - this is an obvious contradiction. Therefore, Vika is a historian. Then Masha is a philologist - otherwise (by condition 3) Vika would be a biologist. Therefore, Anna is a biologist.