Is the relation reflexive, symmetric, transitive

[iHeartof12]

Indicate which of the following relations on the given sets are reflexive on a given set, which are symmetric and which are transitive.

{(x,y)$\in$$ZxZ$: x+y=10}

Tell me if I'm thinking about this correctly

It is not reflexive because the only 5R5.
It is symmetric because any xRy and yRx where x+y=10.
It is not transitive because any xRy and yRx, x is not related to x.

 

[sunjin09]

all correct

 

[iHeartof12]

thank you