I have a question regarding an image. I'm currently studying binary relations and the following image confused me:
What got me confused is that the page from which I got the link (http://www.cs.odu.edu/~toida/nerzic/content/relation/property/property.html) says that the graph in (a) is reflexive, symmetric and transitive.
According to what I've learned so far a set is reflexive if for all $x$, $x$ bears a relation to $x$, the graph has this property. Now, for the other two relations, symmetric and transitive, it does not hold. Because for it to be symmetric it would need a path from both points back to each other (because a relation is symmetric iff $x$ has a relation to $y$ and back). The transitive property also does not hold because there are only 2 points and transitivity needs at least three.
I would like some proof that explains why the graph is transitive and symmetric.