$2.(16$pts$)$ Causal Consistency Model. Consider a data store with four replicas each has one process associated with it$.$ For each of the following scenarios of executions: $($a$)$ identify the causal relations among the write operations; $($b$)$ find out if the executions are possible when the data store implements the causal consistency model; $($c$)$ if not causally consistent, point out which causal relations do not hold; $($d$)$ if causally consistent, further point out if the data store can be sequentially consistent.

$(1)$

P$1$: W$1($x$)$a R$1($x$)$c W$1($x$)$b R$1($x$)$b

P$2$: R$2($x$)$a W$2($x$)$c R$2($x$)$c W$2($x$)$d

P$3$: R$3($x$)$a R$3($x$)$b R$3($x$)$d

P$4$: R$4($x$)$d R$4($x$)$b W$4($x$)$e