[1+2+3 = 6 points] Consider a group of robots in which each robot has a circular sensing range. A robot į can "see" some other robot j whenever j is inside the sensing range of i. Every robot can see itself. We can represent this relation by drawing an arrow from i to j. For instance, see the below figure. Figure: robot i can see robot j. Now, let A be the set of n > 2 robots, and we define a relation R over them as follows: Robot a is related to robot b if and only if a can see b. In other words, (a, b) ER if and only if a can see b. (i) (ii) (iii) If all the robots have the same sensing radius (the radius of sensing circle is same for every robot), then give an example of a robot configuration (placements) such that R is a partial order. Justify your answer. Characterize robot configurations for which R can never be a partial order. You must justify your answer. If all n robots have infinite sensing radius (meaning very large sensing ranges), then (a) show that R will be an equivalence relation. (b) Give an expression (in terms of n) of the number of arrows in the arrow diagram of R. (c) Also, comment on the number of equivalence classes in the relation.