A fictional records-office implication chain
A fictional records office states three rules for this exercise. Every indexed file has a reference number. No file with a reference number is anonymous. Some archived files are indexed. The office has not stated that every archived file is indexed, nor that every numbered file is indexed. Two analysts disagree: one says that all archived files must be nonanonymous, while the other says only that at least one archived file is nonanonymous. Treat the rules as complete premises for a logic problem, not as the real policy of a government institution. A student also wants to infer that an unindexed file is anonymous. Explain the strongest warranted conclusion and distinguish an inverse inference from a valid contrapositive.
1. What follows about at least one archived file?
Read the worked answer
Some archived file is indexed, hence numbered, and therefore nonanonymous. This establishes an existence claim, not a statement about every archived file.
2. Does an unindexed file have to be anonymous?
Read the worked answer
No. The premises allow an unindexed file to have a reference number. Indexed implies numbered does not imply unindexed means unnumbered.
3. What follows if a file is anonymous?
Read the worked answer
It has no reference number under the stated prohibition, and therefore cannot be indexed. This uses the relevant contrapositives.