Lecture 6 - Equivalence Relations Flashcards
1
Q
What is an equivalence relation?
A
A relation on a set that is reflexive, symmetric and transitive.
2
Q
What does an equivalence relation look like in a digraph?
A
Loops on all elements, directed edges from each vertex to each other vertex, in both directions.
3
Q
By looking at a matrix, how can you tell if the relation it represents is reflexive?
A
There are 1’s on the main diagonal.
4
Q
By looking at a matrix, how can you tell if the relation it represents is symmetric?
A
The (i,j)th entry is equal to the (j, i)th entry.
5
Q
By looking at a matrix, how can you tell if the relation it represents is transitive?
A
The (i,j)th entry of A * A is nonzero when the (i,j)th entry of A is nonzero.