Is this what is meant by transitive and nontransitive set?

Transitive:

$~$A = \{ \{ 1,2 \}, \{ 3,4 \}, 1, 2, 3, 4 \}$~$

$~$x = \{1,2\}$~$

$~$a = 2$~$

$~$a \in x$~$, $~$x \in A$~$ and $~$a \in A$~$

Nontransitive:

$~$B = \{ \{ 1,2 \}, \{ 3,4 \} \}$~$

$~$y = \{1,2\}$~$

$~$b = 2$~$

$~$b \in y$~$, $~$y \in B$~$ but $~$b \notin B$~$

## Comments

Kevin Clancy

Yes, that's correct. I wonder if it is even a good idea to talk about transitive sets in the transitive relation page, as most people who are interested in transitive relations are not likely to care about transitive sets. When this page is expanded beyond stub status, I hope that it will focus mostly on transitivity, rather than related concepts such transitive sets, posets, and preorders.