Exercise 6. (46 points) let g be a finite group and h any subgroup of g. (a) (6 points) use set notation to finish the following statement: if g €g then the coset gh is defined as 9h = { (b) (8 points) define the funtion g g/h + g/h by (1,c) 2.c = {tc: cec}. verify that r. c 6g/h, i. e., that r. c is a coset of h, for each reg and c eg/h. (c) (16 points) prove that the function from part (b) defines an action of g on g/h. (a) (16 points) is the action from part (c) transitive? justify your answer.