transitive relation

let $\text{[math]}$ be a relation over set $\text{[math]}$ ( $\text{[math]}$ ), $\text{[math]}$ is a transitive relation if for every $\text{[math]}$ , if $\text{[math]}$ and $\text{[math]}$ then $\text{[math]}$ .

$\text{[math]}$

$\text{[math]}$ isnt transitive $\text{[math]}$ there exist $\text{[math]}$ and $\text{[math]}$ so that $\text{[math]}$