Consider a relation on the set

given by the following digraph.

B

C

D

A

$[$Graphs generated by this script: initPicture$(-100,400,-100,400)$;; marker$=$"arrow";; dot$([150,240])$;; dot$([150,50])$;; dot$([250,-50])$;; dot$([50,200])$;; text$([150,240],\text{'}$B$\text{'},$'below'$)$;; text$([150,50],\text{'}$C$\text{'},$'below'$)$;; text$([250,-50],\text{'}$D$\text{'},$'below'$)$;; text$([50,200],\text{'}$A$\text{'},$'below'$)$;; loop$([250,-50],[250,-50])$;; loop$([150,240],[150,240])$;; loop$([150,50],[150,50])$;; loop$([50,200],[50,200])$;; arc$([150,50],[250,-50])$;; arc$([50,200],[150,240])$;; arc$([150,50],[50,200])$;; arc$([250,-50],[150,50])$;; arc$([150,240],[50,200])$;; arc$([50,200],[150,50])$;; $]$

What properties this relation does not satisfy?

symmetric and transitive

transitive and antisymmetric

reflexive and antisymmetric

reflexive and transitive

What type of relation is$?$

Neither equivalence nor PO

Partial Order

Equivalence