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At the regional hospital, any nurse who is assigned to the intensive care unit (ICU) must have completed the specialized critical care certification. Furthermore, no nurse who has completed the specialized critical care certification is permitted to work shifts longer than 12 hours. It is known that some nurses working on the night shift are assigned to the intensive care unit.

If the statements above are true, which one of the following must also be true?

  1. Some nurses working on the night shift are not permitted to work shifts longer than 12 hours.Answer
  2. B
    Any nurse who has completed the specialized critical care certification is assigned to the intensive care unit.
  3. C
    Nurses who are not assigned to the intensive care unit are permitted to work shifts longer than 12 hours.
  4. D
    Most nurses working on the night shift are assigned to the intensive care unit.
  5. E
    The majority of nurses at the regional hospital are not permitted to work shifts longer than 12 hours.

Answer

Some nurses working on the night shift are not permitted to work shifts longer than 12 hours.
The correct answer properly combines the provided premises. Since any nurse in the ICU must be certified, and no certified nurse can work more than 12 hours, it logically follows that no ICU nurse can work more than 12 hours. Because we are told that some night shift nurses are in the ICU, these particular nurses are absolutely subject to the ICU rules. Therefore, it must be true that some night shift nurses are not permitted to work shifts longer than 12 hours.

Step-by-Step Solution

1
Translate the rules into formal logic.
1. ICU -> Certification. 2. Certification -> NOT >12 hours. 3. Night Shift SOME ICU.
Mapping the statements makes the logical chain and the quantities explicit.
2
Connect the conditional statements.
Since ICU requires Certification, and Certification prevents shifts longer than 12 hours, we can deduce: ICU -> NOT >12 hours.
The transitive property of conditional logic allows us to connect the sufficient condition of the first premise to the necessary condition of the second.
3
Combine the chained conditional with the existential quantifier.
We know at least some night shift nurses are in the ICU. Since ALL ICU nurses are prohibited from working >12 hours, those specific night shift nurses must also be prohibited from working >12 hours.
Applying a universal rule (all ICU nurses) to a specific subgroup (some night shift nurses) yields a valid deduction about that subgroup.

Key Concept

Formal Logic Chaining and Existential Quantifiers
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