1. ## New post about relations

I have another relation problem: "For each of these relations on the set {1,2,3,4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive."

{(1,3), (1,4), (2,3), (2,4), (3,1), (3,4)}

According to the answer key, it has none of the properties. I was thinking it was perhaps antisymmetric and transitive. Why isn't it so?

2. ## Re: New post about relations

Originally Posted by Bashyboy
I have another relation problem: "For each of these relations on the set {1,2,3,4}, decide whether it is reflexive, whether it is symmetric, whether it is antisymmetric, and whether it is transitive."
{(1,3), (1,4), (2,3), (2,4), (3,1), (3,4)}
According to the answer key, it has none of the properties. I was thinking it was perhaps antisymmetric and transitive. Why isn't it so?
It cannot be symmetric because $\displaystyle (3,2)$ is not there.

It cannot be transitive because $\displaystyle (2,3)~\&~(3,1)$ but no $\displaystyle (2,1)$.