Suppose you roll a fair six-sided die once. a. Write the sample space for this experiment. {1, 2, 3, 4, 5, 6} b. For each of the following, tell me whether or not it is a valid partition of the sample space, and if it is not a valid partition, tell me why not. i. {{1, 2}, {3, 4, 5}} ii. {{1}, {2}, {3,4}, {5}, {6}} iii. {{1,2,3,6}, {4,5,6}} iv. {{1}, {2,3,4,5}, {6}, {}}