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Difficulty: MediumDiagramming Conditional Statements

According to a national museum's updated curation protocols, an artifact will be exhibited in the Main Gallery only if it undergoes a comprehensive structural restoration. Furthermore, a comprehensive structural restoration requires the direct supervision of the chief conservator. No artifact can be insured for its maximum appraised value unless it is exhibited in the Main Gallery. Finally, any artifact that lacks a verified historical provenance will not receive the direct supervision of the chief conservator. Based on the rules above, which one of the following statements must be true?

  1. Any artifact that is insured for its maximum appraised value must possess a verified historical provenance.Answer
  2. B
    Any artifact that possesses a verified historical provenance will be insured for its maximum appraised value.
  3. C
    If an artifact is not insured for its maximum appraised value, then it must lack a verified historical provenance.
  4. D
    Receiving the direct supervision of the chief conservator is sufficient to guarantee that an artifact will be exhibited in the Main Gallery.
  5. E
    Most artifacts that undergo a comprehensive structural restoration are eventually insured for their maximum appraised value.

Answer

The statement that any artifact insured for its maximum appraised value must possess a verified historical provenance.
The correct answer accurately synthesizes the conditional statements into a single transitive chain. The stimulus establishes that maximum insurance requires Main Gallery exhibition. Main Gallery exhibition requires restoration. Restoration requires the chief conservator's supervision. Finally, if an artifact lacks provenance, it cannot have supervision, which contraposes to: supervision requires provenance. Chaining these together proves that any artifact insured for maximum value must ultimately have a verified provenance.

Step-by-Step Solution

1
Translate the first conditional statement ('only if').
Exhibited in Main Gallery -> Comprehensive Structural Restoration
The phrase 'only if' introduces a necessary condition.
2
Translate the second conditional statement ('requires').
Comprehensive Structural Restoration -> Direct Supervision of Chief Conservator
The word 'requires' introduces a necessary condition.
3
Translate the third conditional statement ('unless').
Insured for Maximum Value -> Exhibited in Main Gallery
The phrase 'No X unless Y' translates to 'If X, then Y' (or 'If not Y, then not X').
4
Translate and contrapose the final conditional statement.
Original: No Verified Provenance -> No Direct Supervision. Contrapositive: Direct Supervision -> Verified Provenance
To connect this statement to the others, we must take its contrapositive by negating and reversing both terms.
5
Synthesize the individual conditional statements into a single transitive chain.
Insured for Maximum Value -> Exhibited in Main Gallery -> Comprehensive Structural Restoration -> Direct Supervision -> Verified Provenance
Because the necessary condition of each rule matches the sufficient condition of the next, they form a continuous deductive chain.
6
Evaluate the options against the synthesized chain to find the valid inference.
The chain proves that 'Insured for Maximum Value -> Verified Provenance', which matches the correct answer.
In a valid conditional chain, the first sufficient condition guarantees the final necessary condition.

Key Concept

Conditional Logic Chaining and Contraposition
Estimated Time:1m 30s
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Topics

Diagramming Conditional Statements

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