Assume the relation R over the set {0,1,2,3,4,5,6,7,8,9} where (a,b) ∈ R if and only if a+b

1. Assume the relation
   R
   over the set {0,1,2,3,4,5,6,7,8,9} where (a,b) ∈ R if and only if

a+b <>

1. Determine if the relation is Reflexive, symmetric, antisymmetric, or transitive (Use a table).


2. Represent your relation
   R
   by a graph, and specify what type of graph can be used to represent this relation.


3. Determine the degree of each vertex and the total degrees of the graph (Use a table).


4. Determine whether the graph has an Euler circuit. Construct such a circuit when one exists. If no Euler circuit exists, determine whether the graph has an Euler path and construct such a path if one exists.


5. Generate an adjacency matrix for your graph.