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Zorluk: Çok zorStatement and Conclusions or Inferences

Read the policy directives and facts outlined below, then evaluate the subsequent inferences.

Statements:
1. Every municipal budget proposal that allocates funds for urban transport is subject to the immediate review of the State Finance Committee.
2. No proposal reviewed by the State Finance Committee is exempt from the mandatory external audit.
3. The recently drafted Sector 4 zoning plan is exempt from the mandatory external audit.

Conclusions:
I. The recently drafted Sector 4 zoning plan does not allocate funds for urban transport.
II. Any municipal budget proposal that is exempt from the mandatory external audit does not allocate funds for urban transport.

Based on the strictly logical deductions from the above statements, which option is correct?

  1. A
    Only conclusion I follows
  2. Only conclusion II followsCevap
  3. C
    Both conclusion I and conclusion II follow
  4. D
    Neither conclusion I nor conclusion II follows

Cevap

Only conclusion II follows.
The correct answer identifies that only the second inference is a valid logical derivation. From Statement 2, if any proposal is exempt from the external audit, it was not reviewed by the State Finance Committee. Statement 1 dictates that allocating urban transport funds within a municipal budget proposal guarantees this review. Thus, any municipal proposal bypassing the audit cannot possibly contain transport funds, validating Conclusion II. Conclusion I is invalid because the text never classifies the 'Sector 4 zoning plan' as a 'municipal budget proposal', meaning it could be a different type of document that allocates transport funds without triggering the committee's municipal rules.

Adım Adım Çözüm

1
Translate the statements into formal logical conditions.
Statement 1: (Municipal Proposal AND Transport Funds) → SFC Review. Statement 2: SFC Review → NOT Exempt from Audit. Statement 3: Sector 4 Plan → Exempt from Audit.
Formalizing the premises prevents the conflation of similar but distinct categories, which is crucial for high-difficulty deductions.
2
Evaluate Conclusion I using the contrapositive of the statements.
Sector 4 is exempt from the audit, meaning it bypassed SFC review (contrapositive of S2). This implies Sector 4 is NOT a (Municipal Proposal AND Transport Funds). By De Morgan's laws, it is either NOT a municipal proposal OR it does NOT have transport funds. Because the text never states Sector 4 is a municipal proposal, it could theoretically be a state-level plan that DOES fund transport. Conclusion I is invalid.
A valid conclusion must hold strictly true under all possible scenarios permitted by the premises; we cannot assume unstated classifications.
3
Evaluate Conclusion II by chaining the conditional logic.
Take a theoretical municipal proposal that is exempt from the audit. Exemption guarantees it had no SFC review. For a municipal proposal to avoid SFC review, it must NOT allocate transport funds (contrapositive of S1). Conclusion II is logically bulletproof.
Tracking the rigid negative modifiers confirms that the conditions for Conclusion II mathematically satisfy all stated rules.

Anahtar Kavram

Logical Deduction via Contrapositive and Category Boundaries
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Konular

Statement and Conclusions or Inferences

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