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Zorluk: OrtaStatement and Conclusions or Inferences

The following facts are recorded in the annual operations report of a government municipality:

1. All departments that implement the new digital archiving system reduce their paper consumption by half.
2. No department in the grievance redressal wing has reduced its paper consumption by half.
3. Some priority task forces are operating within the grievance redressal wing.

Based strictly on these records, which of the conclusions logically follow? (Select all correct options)

  1. No department in the grievance redressal wing has implemented the new digital archiving system.Cevap
  2. Some priority task forces have not implemented the new digital archiving system.Cevap
  3. C
    Any department that has reduced its paper consumption by half has implemented the new digital archiving system.
  4. D
    The grievance redressal wing handles physical documents that cannot be digitized for legal reasons.

Cevap

The valid inferences are that no department in the grievance redressal wing has implemented the new system, and that some priority task forces have not implemented it.
The valid inferences are derived through direct logical deduction. Because implementing the system always results in reduced paper consumption, any department failing to reduce paper consumption cannot have implemented the system (modus tollens). Since the grievance redressal wing falls into this category, none of its departments use the system. Furthermore, because some priority task forces are part of this wing, they too must not be using the system.

Adım Adım Çözüm

1
Analyze Statement 1 and Statement 2 using conditional logic.
Statement 1 implies: If a department implements Digital Archiving, it reduces paper by half. Statement 2 implies: If a department is in the Grievance Redressal wing, it does NOT reduce paper by half.
Establishing the formal logical relationship between the conditions allows for accurate deductions without relying on assumptions.
2
Derive an overarching conclusion by combining the first two statements.
Applying the contrapositive to Statement 1 (If a department does NOT reduce paper by half, it did NOT implement Digital Archiving), and linking it to Statement 2 yields: No department in the Grievance Redressal wing has implemented Digital Archiving.
This confirms the validity of the first correct conclusion.
3
Incorporate Statement 3 to evaluate specific subsets of departments.
Statement 3 establishes that some Priority Task Forces operate within the Grievance Redressal wing. Because no department in this wing has implemented the system, those specific task forces must not have implemented it either.
This confirms the validity of the second correct conclusion regarding priority task forces.
4
Evaluate the remaining options against the derived logical boundaries.
The option reversing the cause-and-effect of paper reduction is rejected as a formal fallacy. The option proposing legal reasons for document retention is rejected as it relies on outside information.
Strict logical inference prohibits affirming the consequent or injecting external context.

Anahtar Kavram

Applying syllogistic reasoning (modus tollens) to extract valid conclusions and avoiding external knowledge contamination.
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Konular

Statement and Conclusions or Inferences

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