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Consider a demand-paging system in which a process is allocated three memory frames. When a page fault occurs in the process, let p1, p2 and p3 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 a1, a2 and a3 respectively. Let the timestamps of last reference to these pages be r1, r2 and r3 respectively.

Let the Least Recently Used (LRU) page-replacement scheme be employed by the demand-paging system. If p2 is the page that is chosen to be replaced as part of servicing the page fault, determine the relationships among a1, a2, a3, r1, r2 and r3. Based on these relationships, select from the following list the statement that is CERTAIN to be TRUE.

 
  a)  r2 is earlier than a3
  b)  a3 is later than a1
  c)  r3 is later than a2
  d)  a1 is later than r2

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