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Difficulty: MediumIdentifying Must-Be-True Statements and Valid Deductions

At an ongoing archaeological excavation of an ancient Mediterranean trading port, researchers have established two strict origin rules for artifact classification: first, any ceramic vessel containing traces of refined pine resin was manufactured in Coastal Region K. Second, every ceramic vessel manufactured in Coastal Region K that dates to the 4th century BCE features a specialized lead-based sealant glaze.

Statement: Based on the rules above, if an excavated ceramic vessel dates to the 4th century BCE but does not feature a lead-based sealant glaze, it cannot contain traces of refined pine resin.

Answer: Answer

Answer

True. The deduction is logically valid and guaranteed by combining the contrapositives of the two premise rules.
The statement must be true. Combining the given conditional premises demonstrates that any 4th-century BCE vessel with pine resin would necessarily require the lead-based glaze. Therefore, the absence of the glaze on a 4th-century BCE vessel guarantees the absence of pine resin.

Step-by-Step Solution

1
Represent the premises using conditional logic statements.
Rule 1: Pine Resin →\rightarrow Region K. Rule 2: (Region K ∧\land 4th Century BCE) →\rightarrow Lead-based Glaze.
Formalizing the premises clarifies the required chain of logic.
2
Take the contrapositive of Rule 2 for artifacts from the 4th century BCE.
If an artifact is from the 4th century BCE and lacks a Lead-based Glaze, it was NOT manufactured in Region K.
The contrapositive of A→BA \rightarrow B is ¬B→¬A\neg B \rightarrow \neg A, which is logically equivalent.
3
Apply the contrapositive of Rule 1 to the result of Step 2.
Rule 1 Contrapositive: NOT Region K →\rightarrow NO Pine Resin.
Since the artifact was not manufactured in Region K, it cannot possess the characteristic unique to Region K vessels.
4
Synthesize the conclusion.
A 4th-century BCE vessel without lead-based glaze cannot contain refined pine resin. Thus, the statement MUST BE TRUE.
The conclusion is 100% guaranteed by the given premises.

Key Concept

Conditional Logic & Contrapositive Chain Deductions
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Topics

Identifying Must-Be-True Statements and Valid Deductions

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