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Zorluk: Çok zorMost Strongly Supported Questions

Historians analyzing the recently discovered Qumran Archive have established several facts about its manuscripts. Every manuscript in the archive that was written on vellum was authored by a member of the elite scribal class. Furthermore, most of the manuscripts in the archive that were authored by the elite scribal class contain political commentary. However, none of the manuscripts written on papyrus contain any political commentary. All of the manuscripts in the archive were written on either vellum or papyrus.

Which one of the following is most strongly supported by the information above?

  1. A
    None of the manuscripts in the archive written on papyrus were authored by the elite scribal class.
  2. B
    Any manuscript in the archive that does not contain political commentary was written on papyrus.
  3. C
    At least some manuscripts in the archive that were written on vellum do not contain political commentary.
  4. Most of the manuscripts in the archive that were authored by the elite scribal class were written on vellum.Cevap
  5. E
    The elite scribal class chose to write on vellum because papyrus was unsuitable for recording political commentary.

Cevap

Most of the manuscripts in the archive that were authored by the elite scribal class were written on vellum.
Since all manuscripts in the archive are either vellum or papyrus, and none of the papyrus manuscripts contain political commentary, it must be logically true that ALL manuscripts containing political commentary are written on vellum. The stimulus explicitly states that MOST of the manuscripts authored by the elite scribal class contain political commentary. Since all of these political commentary manuscripts are on vellum, it mathematically follows that most of the manuscripts authored by the elite scribal class were written on vellum.

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1
Establish the binary constraint for the manuscript materials.
Every manuscript is either vellum (V) or papyrus (P).
This structural rule dictates that any manuscript that is not papyrus must inherently be vellum.
2
Translate the conditional rules regarding political commentary.
If Papyrus -> No Political Commentary (~PC). By contrapositive, if Political Commentary (PC) -> Not Papyrus. Given Step 1, this means PC -> Vellum.
This establishes a critical bridge: every single manuscript in the archive containing political commentary is written on vellum.
3
Synthesize the quantifier rule with the derived conditional rule.
Most of the elite scribal class manuscripts contain political commentary. Since all political commentary manuscripts are vellum, these 'most' must also be vellum.
When a subset (more than half) possesses a trait, and that trait guarantees membership in a specific category (vellum), then more than half of the original overarching group must belong to that category.

Anahtar Kavram

Logical Synthesis of Quantifiers (Most/Some) with Conditional Contrapositives

Alternatif Yöntem

You can visualize this mathematically. Let E be the total number of elite scribal manuscripts. We know manuscripts with political commentary in this group (E_PC) make up more than 50% of E. Since papyrus manuscripts have no political commentary, all E_PC manuscripts must be vellum. Therefore, the number of vellum elite manuscripts is at least equal to E_PC, which means it is also greater than 50% of E.
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