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Zorluk: OrtaChaining Conditional Statements

A municipal planning board adheres to the following regulations for commercial developments:
- If a development is located in the waterfront zone, it must conduct an ecological impact study.
- Any development that conducts an ecological impact study is mandated to construct shoreline defenses.
- A development is granted a reduced property tax rate only if it is not mandated to construct shoreline defenses.
- Any development that receives a mayoral endorsement is granted a reduced property tax rate.

To validly deduce the conclusion 'If a development is located in the waterfront zone, it does not receive a mayoral endorsement,' arrange the following conditional deductions in the correct logical sequence of the transitive chain. Start with the initial trigger and end with the final deductive step.

  1. 1If a development is located in the waterfront zone, it must conduct an ecological impact study.
  2. 2If a development conducts an ecological impact study, it is mandated to construct shoreline defenses.
  3. 3If a development is mandated to construct shoreline defenses, it is not granted a reduced property tax rate.
  4. 4If a development is not granted a reduced property tax rate, it does not receive a mayoral endorsement.

Cevap

The correct sequence connects the waterfront zone to the lack of mayoral endorsement through a transitive chain involving ecological studies, shoreline defenses, and property tax rates by applying two contrapositives.
The correct sequence builds a valid transitive logic chain. It begins with the initial premise (Waterfront -> Ecological Study), continues to the second premise (Ecological Study -> Shoreline Defenses), utilizes the contrapositive of the third premise (Reduced Tax Rate -> NO Shoreline Defenses becomes Shoreline Defenses -> NO Reduced Tax Rate), and finally utilizes the contrapositive of the fourth premise (Mayoral Endorsement -> Reduced Tax Rate becomes NO Reduced Tax Rate -> NO Mayoral Endorsement).

Adım Adım Çözüm

1
Identify the initial trigger from the required conclusion.
The chain must start with 'Waterfront zone'.
The conclusion we need to prove is 'Waterfront zone -> NO mayoral endorsement'.
2
Apply the first premise.
Waterfront zone -> Ecological impact study.
The rules explicitly state waterfront developments must conduct the study.
3
Chain the second premise.
Ecological impact study -> Shoreline defenses.
The rules explicitly state any development with a study must construct defenses.
4
Derive the contrapositive of the third premise.
Shoreline defenses -> NO reduced property tax rate.
The rule 'Reduced tax rate only if NO shoreline defenses' translates to (Reduced Tax Rate -> NO Shoreline Defenses). The contrapositive is (Shoreline Defenses -> NO Reduced Tax Rate).
5
Derive the contrapositive of the fourth premise.
NO reduced property tax rate -> NO mayoral endorsement.
The rule 'Mayoral endorsement -> Reduced tax rate' translates to (Mayoral Endorsement -> Reduced Tax Rate). The contrapositive is (NO Reduced Tax Rate -> NO Mayoral Endorsement).

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Chaining Conditional Statements
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Chaining Conditional Statements

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