Reflexive: For all x we require that x~x

Symmetric: For all x, y that satisfy x~y, that also y~x

Antisymmetric: For all x, y if x~y and y~x then x = y

Transitive: For all x, y, z if x~y and y~z then x~z

In your case, for example, we know that your relation is not reflexive because there is only one element such that x~x. (ie. a~a, but not b~b and c~c.)

-Dan