You must analyze the rules for how the system should determine a case's eligibility. The structure of these rules can vary very much from product to product.
It is common for eligibility rules to center around the claimant or household falling into a particular category, where each category is determined by the claimant or household meeting a number of conditions. The categories and the rules for each typically form the "highest level" of rules for eligibility.
For some products, the case's overall eligibility can be determined without reference to the entitlement to any objectives; for other products the eligibility and entitlement calculations are much more intertwined (e.g. for some products, you may only want the case to be deemed eligible if one or more objectives are attained). You will need to visit your business requirements to understand the interplay (if any) between eligibility and entitlement calculations for your product.
The eligibility result calculated by the Engine is a Timeline of Boolean results, and thus allows for the eligibility to vary over time. For some simple products, the eligibility on any given day is purely determined by the case's circumstances on that day; however, for some more complex products, the eligibility on one day may be influenced by events that have occurred on other days (e.g. an event that occurred in on a different day in the same month). You should take care to understand your business requirements for applying events that occur on one day to an overall eligibility result for different days.
For more information on CER's support for Timelines, (see "4.5 Handling Data that Changes Over Time" in the Cúram Express Rules Reference Manual)