Please explain the answer to each part.

C and C and S, are coincident with the z axis alyz) 02 da (1) 9) C" (1) 81 (x2) -2019 ) () & 3 002) C" (2) C (2) (a) Determine the reducible representation using the following method. How many unchanged for each operation enter a positive number. How many are in same location but upsidedown, enter a negative number. If all change position enter zero. (3 points) E CA Care Cz Cz" i S4 (b) The in phase combination (as shown in the figure) is Azu symmetry. Use this determine the TWO remaining irreducible representations that sum to this reducible representation. HINT: one must be doubly degenerate Show work. (2 points) (c) Determine what one of the remaining a Ligand Group Orbitals look like using the following sequence. Transform the wavefunction Y1 using all operations listed below. (2 pts) E;C.; C.; Cxtu; C2(1); C3 (2); C3"(1) ; C*"(2) 4 Y Y Y Y Yg i; S4:54; 0; (az); (y2); 02(1); 0(2) em Multiply each by the characters of the appropriate symmetry label and add them together. 12 pts)