1. (25 points) Susan has three small kids, Alice, Bob and Charles. The coming weekend they are planning to go for some fun outing. There are three possible choices - visit to Angrinion Park (A), visit to the biodome, (B), or visit to the cinema (C). Susan can pick only one of the three. Each of the kids , where i E { Alice, Bob, Charles} has a "strict" preference > relation over the choices A, B, C. Susan's preference relation >Susan is derived from the preference relation of her kids. We will now consider two different ways in which Susan derives her preference. (a) (10 points) In the first instance that we consider, Susan's preference > Susan is of the following form: for any pair of alternatives r, y E {A, B, C}, I > Susan y if and only if > >; y for all i = Alice, Bob, Charles. Is the relation, > Susan complete and transitive ? (b) (More difficult) (15 points) In the second instance, Susan's preference relation Susan is derived in the following manner: for any pair of alternatives r, y E {A, B, C}, T > Susan y if and only if at for at least two of her kids i and j, x>;y & x> ; y. In other words, Susan will prefer x over y if at least two of her kids rank r above y. Here i and j are Susan's kids, that is i, j E { Alice, Bob, Charles}. In this instance, is the relation > Susan complete and transitive