Math 310-01/02

11-10-2017

1. A relation is defined on by

Check each axiom for an equivalence relation. If the axiom holds, prove it. If the axiom doesn't hold, give a specific counterexample.

If , then

Hence, . The relation is reflexive.

If and , then

Hence,

Therefore,

The relation is symmetric.

Note that and , because

But

Hence, . The relation is not transitive.

*The trouble with the rat race is that even if you win you're
still a rat.* - *Lily Tomlin*

Copyright 2017 by Bruce Ikenaga