i'm currently working on a mathproblem in "discrete mathematics for computing". I'm a little behind and have some trouble with one question.
"Let ∼ be a relation defined on the nodes on a graph G(N, E), such that u ∼ v if there exists a path from u to v. Show that ∼ is a equivalences relation on N. What is the equivalence classes of ∼?"
So i presume i need to find out if the Relation is Symmetric, reflexive and Transitive. But i'm not really sure how to handle it.
I have G(N,E), which is graph of (nodes, edges). u and v are nodes, and there is a relation ~ between them. is that right?
So it looks like this o------o ?
what you have drawn is a single edge, but the relation itself is about paths between two nodes, i.e. a series of nodes between the two nodes that are all connected by edges.
For this relation what does it mean to be symmetric, reflexive, transitive?