Is this what is meant by transitive and nontransitive set?

Transitive:

$A=\left\{\right\{1,2\},\{3,4\},1,2,3,4\}$

$x=\{1,2\}$

$a=2$

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

Nontransitive:

$B=\left\{\right\{1,2\},\{3,4\left\}\right\}$

$y=\{1,2\}$

$b=2$

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