Relations and Functions: A Digraph of a Transitive Relation

This short video explores what a digraph of a Transitive Relation looks like, from the topic: Sets, Relations, and Functions. Note: the relation R1 should also contain the ordered pair (7, 9), as spotted by HnyB33 below.

[@LagoonLofi]

watching all of these thanks so much

[@JEMA89JEMA]

You need to add (7,9) as an element of the set to make it transitive!

[@sehreshtariq3266]

This is too good. Excellent and clear explanation!

[@njabulomahlalela2912]

You're so good! Thanks a lot

[@sperera5916]

Thank you very much!

[@rdmcnew]

This helps! Thank you

[@israrkhan3881]

Sir... is there an example of transitive relation which will be a function also

[@aiviskri]

Awesome video, great explanation. I was just wondering, what if a relation is something like {(1, 2)}, is it considered transitive because there's only one connection?

[@MathsAndStats]

That relation would be transitive. In fact, it is known as being vacuously transitive. As there re no double hops (x, y) (y, z) there is nothing to test for and so you can never prove it not be transitive and hence we say it is vacuously transitive. Symmetry would be similar, you can have a vacuously symmetric relation. Thanks for the comment. Please share. Kindest regards. Jonathan.

[@HnyB33]

I think you are great but just want to let you know you forgot to add (7, 9) to R1. You probably already realized this but you should put it somewhere in the description or highlight it in the video.

[@MathsAndStats]

Hi HnyB33. You are correct with that observation. I should certainly have included the ordered pair (7, 9) in R1. I will update description to note this. Thanks so much for your comment. Jonathan