Let m be an integer in the set {0,1,2,3,4,5,6,7,8,9}, and consider the following problem: determine m by asking 3-way questions, i. e. questions with at most 3 possible answers. For instance, one could ask which of 3 specific subsets m belongs to. a. Give a decision tree argument showing that at least 3 such questions are necessary in worst case. In other words, prove that no correct algorithm can solve this problem by asking only 2 questions in worst case. b. Design an algorithm that will solve this problem by asking 3 such questions in worst case. Express your algorithm as a decision tree.