: [10 points] Assume that you have two heuristic functions for a specific problem h1, h2. Provide formal arguments to answer the following questions.

a. If you use the minimum value of h1(n) and h2(n) at every state, will the resulting heuristic be admissible? Is it a consistent one?

b. If you use the maximum value of h1(n) and h2(n) at every state, will the resulting heuristic be admissible? Is it a consistent one?

c. If you define the heuristic function h3(n) = h1(n) + (1 ) h2(n), where 0 1, will this be admissible? Will it be consistent?

d. Consider an informed, best-first search algorithm in which the objective function is (n) = (2 ) g(n) + h(n). For what values of is this algorithm guaranteed to be optimal when h is admissible (for the case of TREE-SEARCH)? What kind of search does the resulting algorithm perform when = 0? When = 1? When = 2?