Consider the problem of performing range checks on set expressions in Pascal. Given that a set may contain many elements, some of which may be known at compile time, describe the information that a compiler might maintain in order to track both the elements known to belong to the set and the possible range of unknown elements. Then explain how to update this information for the following set operations: union, intersection, and difference. The goal is to determine (1) when subrange checks can be eliminated at run time and (2) when subrange errors can be reported at compile time. Bear in mind that the compiler cannot do a perfect job: some unnecessary run-time checks will inevitably be performed, and some operations that must always result in errors will not be caught at compile time. The goal is to do as good a job as possible at reasonable cost.