Math 310: Problem set 2

Instructions: This problem set is due Friday, January 20, 2006. Your goal is not only to give correct answers but to communicate your ideas well. Make sure you use good English,
  1. Let S be the set of natural numbers (i.e., the positive integers). Let R be the relation on S such that (m,n) is in R if and only if n is an integer multiple of m (i.e., m evenly divides n). 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 symmetric but not reflexive and not transitive.
  3. Give an example of a relation R on some set S such that S is transitive but not reflexive and not symmetric.