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Difficulty: Very hardDiagramming Conditional Statements

A municipal oversight committee has established the following regulatory framework for new infrastructure contracts:

- A contract mandates union labor only if it bypasses the secondary financial audit.
- Failure to secure comprehensive risk insurance precludes a contract from receiving fast-track funding approval.
- Incorporating an extended public comment period is sufficient to delay the initial project timeline.
- Securing comprehensive risk insurance requires that the contract mandate union labor.
- No contract bypasses the secondary financial audit unless it incorporates an extended public comment period.

Assume a new infrastructure contract receives fast-track funding approval. Based exclusively on the framework above, arrange the following outcomes in the exact logical sequence they must follow to form an unbroken deductive chain of necessary conditions, from the immediate requirement to the final outcome.

  1. 1The contract secures comprehensive risk insurance.
  2. 2The contract mandates union labor.
  3. 3The contract bypasses the secondary financial audit.
  4. 4The contract incorporates an extended public comment period.
  5. 5The initial project timeline is delayed.

Answer

The correct logical sequence of necessary conditions is: secures comprehensive risk insurance, mandates union labor, bypasses the secondary financial audit, incorporates an extended public comment period, and finally, the initial project timeline is delayed.
The sequence is built by accurately translating complex conditional indicators into a transitive logical chain. The trigger is 'fast-track funding approval' (F). The contrapositive of the second rule yields F -> Insurance (I). The fourth rule yields I -> Union Labor (UL). The first rule yields UL -> Bypass Audit (BA). The fifth rule yields BA -> Extended Public Comment (EPC). The third rule yields EPC -> Delayed Timeline (DT). Stringing these together gives the unbroken chain: F -> I -> UL -> BA -> EPC -> DT.

Step-by-Step Solution

1
Analyze the trigger condition and find its immediate necessary outcome using the second rule.
Fast-track funding approval -> Secures comprehensive risk insurance.
The rule 'Failure to secure comprehensive risk insurance precludes a contract from receiving fast-track funding approval' translates to: (~Insurance -> ~Fast-track). Taking the contrapositive yields the valid deduction: (Fast-track -> Insurance).
2
Find the necessary condition for securing comprehensive risk insurance using the fourth rule.
Secures comprehensive risk insurance -> Mandates union labor.
The rule states that securing insurance 'requires' union labor. The term 'requires' always introduces a necessary condition.
3
Determine the necessary condition for mandating union labor using the first rule.
Mandates union labor -> Bypasses secondary financial audit.
The rule uses the phrase 'only if', which introduces a necessary condition. Therefore, 'mandates union labor only if it bypasses the audit' translates to: (Union labor -> Bypasses audit).
4
Identify the necessary condition for bypassing the secondary financial audit using the fifth rule.
Bypasses secondary financial audit -> Incorporates extended public comment period.
The rule structure 'No A unless B' translates logically to 'If A, then B'. Thus, bypassing the audit guarantees the incorporation of the extended public comment period: (Bypasses audit -> Extended public comment).
5
Find the final outcome resulting from the extended public comment period using the third rule.
Incorporates extended public comment period -> Initial project timeline is delayed.
The rule states that the comment period is 'sufficient' to delay the timeline, forming the final link in the chain: (Extended public comment -> Timeline delayed).

Key Concept

Diagramming Conditional Statements

Alternative Method

Instead of diagramming all the rules in isolation first, you can use the 'chain-building' method: start explicitly with the trigger ('fast-track funding approval'), and scan the text specifically for that exact term or its logical negation to find the first link. Repeat this process for each new necessary condition you discover.
Estimated Time:3m 0s
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Topics

Diagramming Conditional Statements

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