1. ## Relations

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.

2. Originally Posted by kurac
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
correct!

2) {(x,x), (y,y)} = reflexsive
incorrect! the correct answer is "neither". note that $\displaystyle (z,z)$ is not in the set. so it's not reflexive.

3) {(x,x) , (y,y), (z,z), (x,z)} = reflexsive
incorrect! reflexive and transitive.

4) A^2 = reflexsive, symmetric, transitive
correct!

5) 0 (empty set) = neither (im not sure on this one)
incorrect! symmetric and transitive but not reflexive.

6) {(x,y), (x,x), (x,z)} = reflexsive
incorrect! transitive.