`IsTransitiveRel( `

`rel` )

`IsTransitiveRel`

returns `true`

if the binary relation `rel` is
transitive and `false`

otherwise.

gap> IsTransitiveRel( Relation( [ [ ], [ 1 ], [ 1, 2 ] ] ) ); true gap> IsTransitiveRel( Relation( [ [ 2, 3 ], [ 1, 3 ], [ 1, 2 ] ] ) ); false

A relation *R subseteq {1, ..., n} x {1, ..., n}* is
**transitive** if *(x, z) in R* whenever *(x, y) in R* and *(y, z) in R*
for some *y in {1, ..., n}*. (See also TransitiveClosure.)