https://math.stackexchange.com/questions/2196858/what-does-a-transitive-set-exactly-imply

Set Relations:

Reflexive

E.g.1 { (1,1),(2,2),(3,3),(4,4) }

E.g.2 { (3,3),(4,4),(5,5) }

Everybody talks to itself.

*Reflexive is always transitive

Symmetric

E.g.1 { (1,2),(2,1) } , if (1,2) then (2,1) must exist.

E.g.2 { (1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3) }

For (1,2,3) multiple (1,2,3):

Transitive

As (a,b) ∈ R and (b,c) ∈ R , then (a,c) ∈ R.