You and one robot are playing a game where you both have your own score. The figure below shows the game tree of your max node followed by the robots nodes for your four different actions. The scores are shown at the leaf nodes with your score always on top and the robots score on the bottom.

The maximum possible score for either player is $10.$

You are trying to maximize your score, and you do not care what score the robot gets.

The robot is trying to minimize the absolute dierence between the two scores.

In the case of a tie, the robot prefers a lower score. For example, the robot prefers $(5,3)$ to $(6,3)$; it prefers $(5,3)$ to $(0,3)$; and it prefers $(3,3)$ to $(5\mathrm{.}5).$

a$)$Fill in the dashed rectangles with the pair of scores preferred by each node of the game trees.b$)$You can save computation time by using pruning in your game tree search. List all the branches that do not need to be explored. Assume that branches are explored from left to right.