Determine for each of the following classes of subsets of {1,..., n}

whether (together with the empty subset) it forms a group under the group operation of the preceding problem: All subsets {i1,...,ir} with

(i) r = 2;

(ii) r = even;

(iii) r divisible by 3;

(iv) Give two other examples of subgroups G0 of G.

Note. A class of such subgroups is discussed by Forsythe and Hartigan (1970).