2. h (n), h (n), hz (n), and h (n) are four heuristic estimates to the distance from node n to the nearest goal node. It is known that hi(n). hz(n), and hz(n) are admissible heuristics, but h4(n) is not known to be admissible. We define other heuristics as combinations of the given heuristics: hs(n) = h (n) + h (n) +hz(n) 3 hi(n) + h (n) +h3(n) + h4n) h6(n) =- h (n) = hi(n) +h2(n) +h3(n) hg(n) = max{h (n), h (n)} he(n) = min{h (n), hz(n)} h10(n) = max{h3(n), h4(n)} h(n) = min{h (n),h,(n)} (2). With no additional information about hy, h2, h3, h4, give a formula that produces a heuristic h that you consider to be better than h1, h2,..., h11 when used by A* algorithm. Answer: 2. h (n), h (n), hz (n), and h (n) are four heuristic estimates to the distance from node n to the nearest goal node. It is known that hi(n). hz(n), and hz(n) are admissible heuristics, but h4(n) is not known to be admissible. We define other heuristics as combinations of the given heuristics: hs(n) = h (n) + h (n) +hz(n) 3 hi(n) + h (n) +h3(n) + h4n) h6(n) =- h (n) = hi(n) +h2(n) +h3(n) hg(n) = max{h (n), h (n)} he(n) = min{h (n), hz(n)} h10(n) = max{h3(n), h4(n)} h(n) = min{h (n),h,(n)} (2). With no additional information about hy, h2, h3, h4, give a formula that produces a heuristic h that you consider to be better than h1, h2,..., h11 when used by A* algorithm