Hi, Im determining which relations are reflexsive, transitive, summetric or antisymmetric on set A = {x,y,z}.

Ive come up with following:

1) {(x,y), (y,x)} = symmetric

2) {(x,x), (y,y)} = reflexsive

3) {(x,x) , (y,y), (z,z), (x,z)} = reflexsive

4) A^2 = reflexsive, symmetric, transitive

5) 0 (empty set) = neither (im not sure on this one)

6) {(x,y), (x,x), (x,z)} = reflexsive

Can somebody please check my answers and provide some help where i have goone wrong? Many thanks.