Match each flawed or incomplete argument regarding the restoration of the Fresco of Verano to the sufficient assumption that, if true, logically guarantees its conclusion.
- The Fresco of Verano will be restored using the newly developed laser-ablation technique. Therefore, the fresco's delicate original pigmentation will not be damaged during the restoration process.Any restoration utilizing the laser-ablation technique leaves the artwork's original pigmentation undamaged.
- If the restoration team applies chemical solvents to the Fresco of Verano, they will damage its original pigmentation. Since the team has decided not to apply chemical solvents, the original pigmentation will remain completely intact.The original pigmentation of the Fresco of Verano will be damaged only if the restoration team applies chemical solvents.
- To successfully preserve the original pigmentation of the Fresco of Verano, the restoration team must completely avoid abrasive scrubbing. Because the team's protocol strictly avoids abrasive scrubbing, the original pigmentation will be successfully preserved.Avoiding abrasive scrubbing is sufficient to ensure the successful preservation of the original pigmentation.
- The Fresco of Verano will be successfully restored only if the mural is permanently relocated to a climate-controlled museum facility. Therefore, it is inevitable that the Fresco of Verano will not be successfully restored.The mural of the Fresco of Verano will not be permanently relocated to a climate-controlled museum facility.
Answer
Argument 1 requires the assumption that laser-ablation leaves pigmentation undamaged. Argument 2 requires the assumption that pigmentation is damaged only if chemical solvents are applied. Argument 3 requires the assumption that avoiding abrasive scrubbing is sufficient to preserve the pigmentation. Argument 4 requires the assumption that the mural will not be relocated to a climate-controlled facility.
Each correct assumption provides the exact logical bridge needed to make its corresponding argument formally valid. For the first argument, it connects the premise directly to the conclusion. For the second and third, it converts flawed conditional deductions (negation and reversal) into valid ones by providing the missing direction of the conditional relationship. For the fourth, it provides the missing factual premise to trigger modus tollens.
Step-by-Step Solution
Key Concept
Sufficient assumptions must provide 100% logical certainty to the conclusion when added to the premises. This often involves completing conditional chains or fixing flawed conditional reasoning (like illegal reversals or negations).