Let G = D5 be the dihedral group of order 10, and let X = {A, B, C, D, E} be the set of vertices of the regular pentagon, and let Y = {, , , , } be the set of sides. Write G = {0, . . . , 4; 1, . . . , 5}, where i is the counter-clockwise rotation by 2i/5 radians, and where 1, . . . , 5 are the reflections with respect to the axes going through A and ; . . . ; and E and (in that order). (a) For each of the five elements x X, find the stabilizer subgroup Gx. (b) For each of the ten elements g G, find the fixed-point set Xg. (c) For each of the five elements y Y , find the stabilizer subgroup Gy. (d) For each of the ten elements g G, find the fixed-point set Yg. (e) Verify Burnside's formula for the number of orbits of G in each of X and Y