_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. Table 15 POSSIBLE STATUS 3, STATUS 4, COMBINATION STATUS 1, STATUS 2, APPLICATION EXAMINATION STATUS 5, OF STATUSES ELIGIBLE APPLIED APPROVED REQUIRED INSURED 1 Yes Yes Yes Yes No 2 Yes Yes Yes No No 3 Yes Yes No Yes No 4 Yes No Yes No No 5 No No No No No The question may be asked why employees who are eligible, who have applied for insurance, who have had their applications approved, and who require no medical examination (combination 2) are yet not insured. The answer is that the rules given do not logically lead to this conclusion. As a matter of fact, there might be additional rules, such as: any sick employee must first return to work; or any period from date of approval of application to the first of the following month must first pass. The first step in putting this problem on the Kalin-Burkhart Logical-Truth Calculator is to rephrase the rules, using the language of the connectives that we have on the machine. The rules rephrased are: _A._ If an employee is insured, then he is eligible, he has applied for insurance, and his application has been approved. IF 5, THEN 1 AND 2 AND 3 _B._ If an employee has applied (under these rules) for insurance, then he is eligible. IF 2, THEN 1 _C._ If an employee is eligible for insurance, has applied, and requires no medical examination, his application is automatically approved. IF 1 AND 2 AND NOT-4, THEN 3 _D._ If an employee’s application has been approved, then he has applied. IF 3, THEN 2 _E._ If an employee is not eligible, then he does not require a medical examination (under these rules). IF NOT-1, THEN NOT-4 To get the answer we seek, we must add one more rule _for this answer only_: _F._ The employee is not insured. NOT-5