Set relation: is it reflexive, symmetric or transitive?

Hi

First time doing sets and relations in discrete Maths.

If S={2,4,6} and R is a relation defined on S so that R={(2,2),(2,4),(4,2),(4,6)}

Is R reflexive, symmetric or transitive?

I don't know if a relation can be all 3 as there are elements for all three.

I'm ruling out reflexive since it is not true for all xRx but I'm not sure about the other two.

If I'm going with gut feeling alone, I'd say it's transitive based only on the fact that there isn't enough elements in R for me to confidently say it's symmetric.

Can a relation be symmetric and transitive? Also is it transitive?

So would it be correct to state it is symmetric as we have (2,4) and (4,2) and no conflicting elements? Still a little confused about how to treat (4,6)

And that we can rule out transitive as it lacks (2,6) to complete xRy, yRz, and xRz?

That's what I was confused about from ghostwalker. I wasn't sure what "The condtion of symmetry does not require every combination (a,b)." meant.

Ok, so seeing as (6,4) is not present it is not symmetric.

Which now brings me to a new question, can a relation be neither reflexive, symmetric or transitive? Seeing as there is not enough elements in R to show otherwise???