# Thread: please help..

1. ## please help..

Show that a relation R on a set X is symmetric if and only if whenever there is a directed edge from x to y in the digraph of R, there is a directed edge from y to x in the digraph of R.(i don't have the slightest idea how to do this...)

2. Originally Posted by kodirl
Show that a relation R on a set X is symmetric if and only if whenever there is a directed edge from x to y in the digraph of R, there is a directed edge from y to x in the digraph of R.(i don't have the slightest idea how to do this...)
A relation R on a set X is a set of some ordered pairs of $X^2$.
Therefore, you can talk about G=(X,R) as a graph. But since R is symmetric on X you have that xy is in R (that means an edge in this digraph) means that yx is in E(G) too because of symetrry (that means an edge in this digraph).