The first thing to understand is that a relation on A is going to be a subset of AxA, where AxA is the set of all possible ordered pairs whose components come from A (e.g. AxA={(1,1), (1,2), (1,3), (2,1), ... , (3,2), (3,3)}).

A relation can be any subset of AxA, but we have to chose specific elements in order to classify our relation as symmetric, reflexive or transitive.

A reflexive relation must contain the element (a,a) for every a in A. In our example any relation that contains {(1,1), (2,2), (3,3)} will be reflexive.

A symmetric relation that contains (a,b) must also include (b,a). In our example this means that if, for example, your symmetric relation contained the element (2,3) then it must also contain the element (3,2).

A transitive relation that contains (a,b) and (b,c) must also contain (a,c). So if you chose a relation that contained (2,3) and (3,1), then it must also contain (2,1)