$($d$)$ Let $A=\{0,1,2,3\},$ and define a relation $R_4$ on $A$ as follows: $R_4=\{(0,0),(1,0),(1,2),(1,3),(2,0),(2,1),(3,2),(3,0)\}.$

$($i$)$ Which of the following is the directed graph of $R_4?$

$i$ C

$($i$)$

$($ii$)$ Is $R_4$ antisymmetric?

$,$ because $(?$hat$(v),?$hat$(v))in{R}_4$ and $(?$hat$(v),?$hat$(v))?$hat$(v)R_4,$ and $?$hat$(v)?$hat$(v)?$hat$(v).$