A Complete and Concrete Example
The reader may still be wondering when he will see a complete and concrete example of the application of the logical-truth calculator. So far we have given only pieces of examples in order to illustrate some explanation. Therefore, let us consider now the following problem:
Problem. The A. A. Adams Co., Inc., has about 1000 employees. About 600 of them are insured under a contract for group insurance with the I. I. Insurance Co. Mr. Adams decides that more of his employees ought to be insured. As a part of his study of the change, he asks his manager in charge of the group insurance plan, “What are the possible statuses of my employees who are not insured?”
The manager replies, “I can tell you the names of the men who are not insured, and all the data you may want to know about them.”
Mr. Adams says, “No, John, that won’t be enough, for I need to know whether there are any groups or classes that for some basic reason I should exclude from the change I am considering.”
So the manager goes to work with the following 5 statuses and the following 5 rules, and he produces the following answer. Our question is, “Is he right, or has he made a mistake?”
Statuses. A status for any employee is a report about that employee, answering all the following 5 questions with “yes” or “no.”
1. Is the employee eligible for insurance?
2. Has the employee applied for insurance?
3. Has the employee’s application for insurance been approved?
4. Does the employee require a medical examination for insurance?
5. Is the employee insured?
Rules. The rules applying to employees are:
A. Any employee, to be insured, must be eligible for insurance, must make application for insurance, and must have such application for insurance approved.
B. Only eligible employees may apply for insurance.
C. The application of any person eligible for insurance without medical examination is automatically approved.
D. (Naturally) an application can be approved only if the application is made.
E. (Naturally) a medical examination will not be required from any person not eligible for insurance.
Answer by the Manager. There are 5 possible combinations of statuses for employees who are not insured, as shown in Table 15.