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Difficulty: HardMust Be True / Most Strongly Supported

Archaeometrists analyzing decorated terracotta vessels excavated from the Bronze Age settlement of Kalavasos established the following facts:

• Every vessel containing calcite-tempered fabric was manufactured in the Vasilikos Valley.
• No vessel manufactured in the Vasilikos Valley was decorated using hematite-based slip unless it was fired in a reduction-atmosphere kiln.
• Every vessel fired in a reduction-atmosphere kiln displays a distinctive grey core.
• Some vessels excavated from Kalavasos that contain calcite-tempered fabric were decorated using hematite-based slip.
• No vessel displaying a distinctive grey core was glazed with alkaline flux.

If the statements above are true, which of the following statements must also be true? (Select all that apply.)

  1. At least some vessels excavated from Kalavasos display a distinctive grey core and were not glazed with alkaline flux.Answer
  2. B
    Every vessel excavated from Kalavasos that displays a distinctive grey core contains calcite-tempered fabric.
  3. Any vessel manufactured in the Vasilikos Valley that was glazed with alkaline flux was not decorated using hematite-based slip.Answer
  4. D
    No vessel manufactured outside the Vasilikos Valley was fired in a reduction-atmosphere kiln.
  5. E
    All vessels decorated using hematite-based slip contain calcite-tempered fabric.

Answer

The statements that must be true are that at least some vessels excavated from Kalavasos display a distinctive grey core and were not glazed with alkaline flux, and that any vessel manufactured in the Vasilikos Valley that was glazed with alkaline flux was not decorated using hematite-based slip.
The stimulus confirms the existence of Kalavasos vessels that have both calcite fabric and hematite decoration. Chaining the conditional premises demonstrates that these specific vessels must have been made in the Vasilikos Valley, fired in a reduction kiln, possess a grey core, and lack alkaline flux glazing. Furthermore, combining the rules (Vasilikos and Hematite →\rightarrow Reduction Kiln →\rightarrow Grey Core →\rightarrow No Alkaline Flux) yields the contrapositive rule that any Vasilikos vessel glazed with alkaline flux cannot have hematite decoration.

Step-by-Step Solution

1
Map the conditional rules and existential statement provided in the stimulus.
1. Calcite →\rightarrow Vasilikos; 2. Vasilikos + Hematite →\rightarrow Reduction Kiln; 3. Reduction Kiln →\rightarrow Grey Core; 4. Some Kalavasos are Calcite + Hematite; 5. Grey Core →\rightarrow NOT Alkaline Flux.
Translating natural language premises into formal logic prevents scope errors and invalid inferences.
2
Trace the existential premise through the chain of universal conditionals.
There exists a subset of Kalavasos vessels that have Calcite + Hematite. Since they have Calcite, they are Vasilikos. Since they are Vasilikos + Hematite, they were fired in a Reduction Kiln. Therefore, they have a Grey Core and are NOT glazed with Alkaline Flux.
Deduces what properties must belong to the specific vessels confirmed to exist.
3
Derive the contrapositive of the combined conditional relationship.
From (Vasilikos + Hematite →\rightarrow NOT Alkaline Flux), the contrapositive gives (Vasilikos + Alkaline Flux →\rightarrow NOT Hematite).
Determines the necessary exclusion governing Vasilikos vessels that possess alkaline flux glazing.

Key Concept

Formal conditional chaining, quantifier instantiation (some to all deductions), and contrapositive derivation.
Estimated Time:2m 15s
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Topics

Must Be True / Most Strongly Supported

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