Using rules R$1$ through R$4,$ establish a $""$ relationship between the following pairs of events:

$($i$)$ a$1$ and d$0,($ii$)$ b$1$ and d$5,($iii$)$ a$2$ and a$5,($iv$)$ a $3$ and d$4,$ and $($v$)$ a$0$ and c$4.$ Indicate the rule that you apply in establishing a relationship.

$($R$1)ab$ if events a and $b$ are in the same node i and $a$baibja$baccba||bnot(ab)not(ab)Ci(a)$

$(R2)abif$ event $ain$ node $iis$ sending $of$ a message and event $bin$ node $jis$ receiving $of$ the same message

$(R3)abifac$ and $cb$

$(R4)a||bif$ not$(ab)$ and not$(ab)$

Explain the problem thoroughly as well.