3) Please answer full question (a & b) showing detailed work for thumbs up.

a) If you are given a problem described using a state space representation and you add 20 to the cost of each action, will the optimal solution be the same as the one with the original costs? Show an example on a state space of your choice and explain what happens in general.

b) If instead of adding 20 to the costs of each actions you double the costs, will the optimal solution be the same as the one with the original costs? Show an example on a state space of your choice and explain what happens in general.