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Zorluk: Çok zorDiagramming Conditional Statements

According to the university's revised grant allocation rules, a research proposal is designated as a 'Priority-1' initiative only if it demonstrates formal interdisciplinary collaboration. Formal interdisciplinary collaboration is achieved if, and only if, the project team includes researchers from at least three distinct faculties. Furthermore, any project team that includes researchers from at least three distinct faculties requires a dedicated administrative manager, unless the proposal's principal investigator holds a tenured professorship. Finally, no proposal can be designated as a 'Priority-1' initiative if it relies on external corporate funding.

Which one of the following conclusions can be properly drawn from the university's revised grant allocation rules?

  1. A
    If a research proposal demonstrates formal interdisciplinary collaboration and does not rely on external corporate funding, then it will be designated as a 'Priority-1' initiative.
  2. B
    If a project team either lacks a dedicated administrative manager or lacks a tenured principal investigator, then the team cannot include researchers from at least three distinct faculties.
  3. If a proposal whose principal investigator does not hold a tenured professorship is designated as a 'Priority-1' initiative, then the project team requires a dedicated administrative manager and the proposal cannot rely on external corporate funding.Cevap
  4. D
    If a research proposal does not demonstrate formal interdisciplinary collaboration, then its project team cannot include researchers from at least three distinct faculties, nor can it require a dedicated administrative manager.
  5. E
    Proposals that rely on external corporate funding are less likely to achieve formal interdisciplinary collaboration than those funded entirely by the university.

Cevap

The conclusion stating that a 'Priority-1' proposal without a tenured principal investigator must require a dedicated administrative manager and cannot rely on external corporate funding is the correct deduction.
The correct answer seamlessly synthesizes all four rules into a single valid deduction. The stimulus establishes that a 'Priority-1' designation triggers a chain of requirements: it absolutely requires 'interdisciplinary collaboration', which means it strictly requires 'three distinct faculties'. Having 'three distinct faculties' requires at least one of two things: a 'dedicated administrative manager' or a 'tenured principal investigator'. If the proposal lacks a 'tenured principal investigator', it is mathematically forced to satisfy the other half of the requirement, thus needing a 'dedicated administrative manager'. Concurrently, the final rule guarantees that a 'Priority-1' designation completely precludes 'external corporate funding'.

Adım Adım Çözüm

1
Translate the conditional statements into symbolic logic.
1) Priority-1 (P1) -> Interdisciplinary Collaboration (IC). 2) IC <-> Three Faculties (3F). 3) 3F -> (Dedicated Manager (DM) OR Tenured PI (TP)). 4) Corporate Funding (CF) -> ~P1 (Contrapositive: P1 -> ~CF).
Formalizing the text prevents the misinterpretation of complex indicator words like 'only if', 'if and only if', and 'unless'.
2
Chain the conditional statements together where the necessary condition of one matches the sufficient condition of another.
P1 -> IC <-> 3F -> (DM OR TP). Additionally, P1 -> ~CF.
Creating a deductive chain reveals the absolute downstream requirements triggered by any given sufficient condition.
3
Evaluate the correct answer by applying its specific sufficient conditions (P1 and ~TP) to the established chain.
If P1 is true, then 3F must be true, which subsequently requires either DM or TP to be true. Since ~TP is given by the answer choice, DM must logically be true. Also, since P1 is true, ~CF must be true. Therefore, P1 + ~TP strictly guarantees DM + ~CF.
This confirms that the correct answer is an unbroken, valid deduction directly supported by combining all the premises.

Anahtar Kavram

Diagramming and synthesizing complex conditional chains involving compound sufficient/necessary conditions and 'unless' indicators.
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Konular

Diagramming Conditional Statements

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