Assignment:
Consider the usual action of on the set {1, 2,3,4, 5 }, and define an action of on the set of all 2-element subsets of {1, 2, . . . ,5 } by r. {i,j } = {r.i, r.j} (so, for example, r. {1, 3} = {r .1, r .3} = {2, 4}).
={D10 = 1, r, r2, r3, r4, s, sr,sr2,sr3,sr4 } and r4 =s2= 1
1 ) Find all the 2-element sets that are fixed by the element r
(i.e., the sets such that r. {i, j} ={i, j}).
2) Find all the 2-element sets that map the set {1,2}to the set{1,3}.
Provide complete and step by step solution for the question and show calculations and use formulas.