Does S has to be transitive?

Question

Let R,S be relations over A when R is a partially ordered set, S is a s symmetrical relation $R \subset S$. Does S has to be transitive?

Thanks in advance!

Did you try anything to answer this question on your own? (The -1 is from me.) Also, I guess you mean that $A$ is partially ordered by $R$. — martin.koeberl, Mar 23 '17 at 15:46

score 1 · Answer 1 · answered Mar 23 '17 at 15:46

1

$A=\{0,1,2\}$, $R=\emptyset$, $S=\{(0,1),(1,0), (1,2), (2,1)\}$ seems to me to be a counterexample.

answered Mar 23 '17 at 15:46

1 Answers1