Consider a demand$-$paging system in which a process is allocated three memory frames. When a page fault occurs in the process, let p$1,$ p$2$ and p$3$ be the three pages of the process that are resident in memory. Let the timestamps of arrival $($i$.$e$.,$ the time at which the page was loaded most recently$)$ for these three pages be a$1,$ a$2$ and a$3$ respectively. Let the timestamps of last reference to these pages be $\backslash (\backslash$mathrm$\{$r$\}1,\backslash$mathrm$\{$r$\}2\backslash )$ and r $3$ respectively.

Let the Least Recently Used $($LRU$)$ page$-$replacement scheme be employed by the demandpaging system. If p$2$ is the page that is chosen to be replaced as part of servicing the page fault, determine the relationships among a$1,$ a$2,$ a$3,$ r$1,$ r$2$ and r$3.$ Based on these relationships, select from the following list the statement that is CERTAIN to be TRUE.

$\backslash ($ r $1\backslash )$ is earlier than r$3$

$\backslash ($ r $3\backslash )$ is earlier than r$1$

r$2$ is later than r$3$

$\backslash ($ r $1\backslash )$ is later than r$2$