A finite binary relation over a set S can be represented in ML by a list of $2-$tuples. Write an ML function transitive that checks whether a relation is transitive.

You may define auxiliary functions. For instance,

$-$ transitive;

val it $=$ fn : $($a $*$a$)$ list $->$ bool

$-$ transitive nil;

val it $=$ true : bool

$-$ transitive $[(1,1)]$;

val it $=$ true : bool

$-$ transitive $[(1,2),(1,4),(1,3)]$;

val it $=$ true : bool

$-$ transitive $[(1,2),(1,4),(2,3)]$;

val it $=$ false : bool

$-$ transitive $[(1,2),(1,4),(2,3),(1,3)]$;

val it $=$ true : bool