: For each of the following relations on the set R of real numbers, indicate whether that relation satisfies each of the following properties: reflexive, symmetric, transitive and antisymmetric. For each relation, indicate whether it is an equivalence relation or a partial order. If it is a partial order, indicate whether it is a total order. If it is an equivalence relation, describe its equivalence classes.

a. x R y xy 0

b. x R y x > y

c. x R y |x| = |y|

Please indicate your answers in the following table:

	Reflexive	Symmetric	Transitive	Anti-symmetric	Equivalence Relation	Partial Order	Total Order
a
b
c

Describe equivalence classes of equivalence relations (if any) below: