Question on how to tell if its reflective, symmetric, antisymmetric, & transitive?

If I have t his:

x + y = 0

How do I tell if its: Reflective, Symmetric, Antisymmetric, and Transitive?

For Reflective, it says: check f(x,x) = 0

For symmetry, it says: check f(x,y) = f(y,x)

For Transitive, it says: check f(x,y)=0 and f(y,z)=0, then f(x,z)=0

What is Antisymmetric?

This is where I am getting this at: Is the x^2 - xy +2x -2y= 0 reflective/symmetric/transitive??? - Yahoo! Answers

(Look at User JCS)

__________________________________________________ _____________

Am I doing this correct?

f(x, x) = x + y

= x + x

Reflective

f(y, x ) = x + y

= y + x

Symmetry

I am not sure on transitive and i do not know antisymmetric?