1. Let X = Z+, the set of nonnegative integers. In each of the following parts, we will name a binary relation on X. For each one, tell me (i) whether or not it is complete, (ii) whether or not it is transitive, (iii) whether or not it is a preference relation, and if so, (iv) whether or not it admits a utility representation. Justify 370111" answers . (a) The relation 2. (b) The relation 7Q. (c) The relation YES where mYESy for every :I: and y. (d) The relation NOPE where we don't have (ENDPEy for any :13 and y. (e) The relation i3: where :c E; y if and only if either :1: : 0 or a: 2 y 2 1