## 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,
- 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.
- Give an example of a relation R on some set S such that
S is symmetric but not reflexive and not transitive.
- Give an example of a relation R on some set S such that
S is transitive but not reflexive and not symmetric.