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Difficulty: MediumDrawing Valid Inferences

A five-year study of ancient papyrus scrolls from the Ptolemaic period established that every authenticated royal decree issued between 250 BCE and 200 BCE bore the official seal of either the High Chancellor or the Royal Vizier, but never both. The study also revealed that any decree bearing the seal of the High Chancellor was recorded in Greek, whereas any decree addressing agricultural taxation was recorded exclusively in Demotic. Furthermore, during this fifty-year period, no decree recorded in Demotic was validated by the High Chancellor.

Consider each of the three choices separately and select all that apply. Which of the following inferences can be validly drawn from the passage above?

  1. No royal decree issued between 250 BCE and 200 BCE that addressed agricultural taxation bore the seal of the High Chancellor.Answer
  2. B
    Every royal decree issued between 250 BCE and 200 BCE that was recorded in Greek was validated by the seal of the High Chancellor.
  3. Any royal decree issued between 250 BCE and 200 BCE that addressed agricultural taxation bore the seal of the Royal Vizier.Answer

Answer

The statements claiming that no agricultural taxation decree bore the High Chancellor's seal, and that any agricultural taxation decree bore the Royal Vizier's seal, can both be validly drawn.
The inference that no agricultural taxation decree bore the High Chancellor's seal is logically guaranteed because agricultural taxation decrees were written in Demotic, and Demotic decrees were never validated by the High Chancellor. Furthermore, because every decree was required to bear either the High Chancellor's or the Royal Vizier's seal (and never both), any taxation decree lacking the High Chancellor's seal must have been validated by the Royal Vizier.

Step-by-Step Solution

1
Formalize the conditional premises from the passage.
1. Every decree has either the High Chancellor seal or the Royal Vizier seal (mutually exclusive).
2. High Chancellor seal implies Greek language.
3. Agricultural taxation implies Demotic language.
4. Demotic language implies NOT High Chancellor seal.
Establishing explicit symbolic logic rules prevents misinterpreting conditional relationships.
2
Evaluate the relationship between agricultural taxation decrees and the High Chancellor seal.
Combining premise 3 and premise 4 shows that Agricultural taxation implies Demotic, which implies NOT High Chancellor seal. Thus, no taxation decree bore the High Chancellor seal.
Valid hypothetical syllogism connecting agricultural taxation to the absence of the High Chancellor seal.
3
Evaluate the seal requirement for agricultural taxation decrees.
Since every decree must have either the High Chancellor seal or the Royal Vizier seal, and taxation decrees lacked the High Chancellor seal, all taxation decrees necessarily bore the Royal Vizier seal.
Deductive elimination based on the exhaustive seal rule.
4
Evaluate the statement concerning decrees written in Greek.
High Chancellor seal implies Greek language does not mean Greek language implies High Chancellor seal. Other decrees could also be written in Greek.
Prevents committing the logical fallacy of affirming the consequent.

Key Concept

Drawing Valid Inferences via Conditional Logic and Categorical Deduction
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Drawing Valid Inferences

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