# Relations

• May 3rd 2009, 06:25 PM
kurac
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.
• May 3rd 2009, 08:22 PM
NonCommAlg
Quote:

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!

Quote:

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.

Quote:

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

incorrect! reflexive and transitive.

Quote:

4) A^2 = reflexsive, symmetric, transitive

correct!

Quote:

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

incorrect! symmetric and transitive but not reflexive.

Quote:

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

incorrect! transitive.