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Zorluk: Çok zorChaining Conditional Statements

According to the new municipal regulations, the city council will authorize a tax abatement for a new project only if the project's commercial development phase proceeds. However, the commercial development phase will not proceed unless a zoning variance is granted. Furthermore, the commercial phase proceeds only if an environmental impact study is fully approved. The environmental impact study will be fully approved only when the local conservation group does not file a petition against the project. It is well known that the local conservation group will file a petition against any project unless the local wildlife habitat is strictly preserved and public access to the shoreline is maintained.

Based on the municipal regulations described above, which one of the following must be true?

  1. A
    If a zoning variance is granted for a project, its commercial development phase will proceed.
  2. B
    If a project fails to strictly preserve the local wildlife habitat but maintains public access to the shoreline, the local conservation group will not file a petition against it.
  3. If a project does not strictly preserve the local wildlife habitat, the city council will not authorize a tax abatement for it.Cevap
  4. D
    If a project's local wildlife habitat is strictly preserved and public access to the shoreline is maintained, the city council will authorize a tax abatement for the project.
  5. E
    If the local conservation group files a petition against a project, a zoning variance for that project will not be granted.

Cevap

If a project does not strictly preserve the local wildlife habitat, the city council will not authorize a tax abatement for it.
The correct answer accurately traces the contrapositive of the entire conditional chain. The stimulus establishes that a tax abatement requires the commercial phase to proceed, which requires the environmental study to be approved, which requires no petition to be filed. A petition is avoided ONLY IF the habitat is strictly preserved AND public access is maintained. Therefore, if the habitat is not strictly preserved, the compound necessary condition fails. This triggers the petition, which prevents study approval, stopping the commercial phase, and ultimately ensuring the city council will not authorize the tax abatement.

Adım Adım Çözüm

1
Translate the first three conditional statements establishing the requirements for the tax abatement and commercial development.
Tax Abatement (TA) -> Commercial Development proceeds (CD). CD -> Zoning Variance Granted (ZVG). CD -> Environmental Impact Approved (EIA).
Identifying the baseline sufficient-necessary relationships, noting that 'only if' and 'unless' introduce necessary conditions.
2
Translate the final two statements regarding the environmental study and the conservation group.
EIA -> No Petition filed (~CGP). Not (Preserved AND Maintained) -> Petition filed (CGP).
The 'unless' clause modifies a compound condition. 'Unless X and Y' means 'If not (X and Y)'.
3
Form the contrapositive of the final compound condition.
~CGP -> (Local Wildlife Preserved AND Public Access Maintained).
This puts the statement in a format that can link directly to the end of the previous conditional chain.
4
Chain all the conditional statements together to see the full logical sequence.
TA -> CD -> EIA -> ~CGP -> (Preserved AND Maintained). Note that CD -> ZVG is also true but branches off.
Connecting the necessary condition of one statement to the sufficient condition of the next reveals the overarching logical architecture.
5
Form the contrapositive of the entire chain to find the correct valid inference.
Not (Preserved AND Maintained) -> CGP -> ~EIA -> ~CD -> ~TA.
Since 'Not (Preserved AND Maintained)' means 'Not Preserved OR Not Maintained', failing to meet EITHER condition triggers the entire negative chain, guaranteeing the tax abatement is denied.

Anahtar Kavram

Chaining Conditional Statements with Compound 'Unless' Clauses
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Chaining Conditional Statements

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