$\def\R{\mathrel R}$A relation $R$ is transitive if $a\R b$ and $b\R a$ implies $a\R c$
because it is never $a\R b$ and $b\R a$, it is always true because no matter what $a\R c$ is, if the LHS is false, the statement is always true.
$\def\R{\mathrel R}$A relation $R$ is transitive if $a\R b$ and $b\R a$ implies $a\R c$
because it is never $a\R b$ and $b\R a$, it is always true because no matter what $a\R c$ is, if the LHS is false, the statement is always true.