Let S={1,2,3,…,n}. Consider a function f:S→S. A subset D of S is said to be invariant if for all x∈D we have f(x)∈D. The empty set and S are also considered as invariant subsets. By deg(f) we define the number of invariant subsets D of S for the function f.i) Show that there exists a function f:S→S such that deg(f)=2.ii) Show that for every 1≤k≤n there exists a function f:S→S such that deg(f)=2k. functioninvariantalgebra unsolvedalgebracombinatorics