I need help solving these 5 questions.

81 5.2 Relations Prove the generalization of DeMorgan's laws to any finite collection of sets: AnA2nAArUA2U.UAn, Prove the generalization of equation (5.3), which is called the principle of inclusion and exclusion: AIA -Ai n A2l-IAi n Al-..(all pairs) (all triples) Show that the set of odd natural numbers is countable. Show that for any finite set S, the power set 25 has 2/51 elements (that is, there are 2l51 distinct subsets of S). Give an inductive definition for an n-tuple by extending the set-theoretic definition for an ordered pair