Match each access policy for the National Historical Archive on the left with its logically valid contrapositive on the right.
- A researcher cannot access the restricted vault unless they possess a faculty sponsor and a valid security clearance.If a researcher lacks a faculty sponsor or lacks a valid security clearance, they are prohibited from accessing the restricted vault.
- An artifact may be photographed only if it is fully restored or encased in protective glass.If an artifact is neither fully restored nor encased in protective glass, it cannot be photographed.
- Having a certified archivist present is a necessary requirement to open the sealed manuscripts.If there is no certified archivist present, the sealed manuscripts cannot be opened.
- Provided that a document is both fragile and heavily redacted, it will not be exhibited to the public.If a document is exhibited to the public, it must be either not fragile or not heavily redacted.
Answer
The correct pairings link each conditional statement to its logically equivalent contrapositive, paying close attention to De Morgan's laws for compound conditions.
Each matching pair accurately translates the natural language indicator words ('unless', 'only if', 'necessary', 'provided that') into a formal conditional relationship, then correctly reverses and negates both sides. For policies involving compound conditions, De Morgan's laws are correctly applied to switch 'and' to 'or' and vice versa.
Step-by-Step Solution
Key Concept
Forming logically valid contrapositives, including the application of De Morgan's laws to compound conditional statements.