5) Please answer full question showing detailed work for thumbs up.

Suppose you have two admissible heuristics, h1 and h2. You decide to create the following new heuristic functions defined as follows:

h3(n) = max(h1(n), h2(n))

h4(n) = max(h1(n), 1.1 * h2(n))

h5(n) = min(h1(n), 3Explain * h2(n))

h6(n) = h1(n) + h2(n)

h7(n) = (h1(n) + h2(n)) / 2

For each of the new heuristics specify of it is admissible or not. Justify your answer. For the new heuristics h2(n) to h7(n), if they are admissible, would you use them instead of using h1 or h2? why (or why not)?