Math 310: Problem set 1

Instructions: This problem set is due Friday, January 13, 2006. Your goal is not only to give correct answers but to communicate your ideas well. Make sure you use good English,
  1. Consider the relation R = { (a, b) : a and b are integers and a - b < 1} on the set S = Z of integers. For each of the three properties of an equivalence relation, either show the property holds, or given an example for which it does not hold.
  2. Give an example of a relation R on some set S such that S is reflexive and transitive but not symmetric.