1. Check whether or not each of the following binary relations on a set X is a preference relation (i.e., is complete and transitive). Justify your answers. (a) X = Rand x _ y if x - y> 1. (b) X = R and x -1. (c) X is the set of people in the world, and x _ y if a was born on or before the same day as y. (d) X is the set of countries in the world, and x _ y if x and y share a border. (e) X is the set of products at the grocery store, and x ~ y if either x has at least as many calories as y or x costs as least as much as y