For any two non-empty subsets of R let us write P<=Q if , for each x in P, there is a y in Q satisfying x<=y

(a) Show that if P<=Q then supP<= supQ (sup is short for supremum)

(b) Give an Example to show that if P<=Q then it does not follow that infP<=infQ (inf is short for infimum)

(c) Give an example to show that if P<=Q and if Q<=P then it does not follow that P=Q