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