This is Analysis.

Please answer all three parts of the question clearly showing all the work.

Problem 5. For the following sets 5' of rational numbers, determine whether: (a) S has a supremum in Q; (h) S has an inmum in Q; (c) S has a supremum in R; (d) S has an inmum in R. If any of these exist, give their values. Prove your answers. (i) S = {27:11 :n E N} (ii)S={mEQ:0