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Difficulty: MediumDiagramming Conditional Statements

According to the recently ratified Global Agricultural Trade Pact, a nation is permitted to export genetically modified crops only if it maintains a centralized agricultural registry. Furthermore, maintaining such a registry requires the nation to pass the Environmental Baseline Audit. No nation passes the Environmental Baseline Audit without successfully implementing strict cross-pollination containment protocols. Finally, establishing an independent monitoring commission is prerequisite to successfully implementing these strict cross-pollination containment protocols.

Based on the rules provided, arrange the following conditions in the correct logical sequence to form an unbroken, valid deductive chain. Begin with the initial sufficient condition for the sequence and conclude with the final necessary condition.

  1. 1The nation is permitted to export genetically modified crops.
  2. 2The nation maintains a centralized agricultural registry.
  3. 3The nation passes the Environmental Baseline Audit.
  4. 4The nation successfully implements strict cross-pollination containment protocols.
  5. 5The nation establishes an independent monitoring commission.

Answer

The correct logical sequence from initial sufficient condition to final necessary condition is: Exporting crops → Maintaining registry → Passing audit → Implementing containment → Establishing commission.
The correct sequence accurately translates each conditional indicator to form an unbroken deductive chain. 'Only if' makes the registry necessary for exporting; 'requires' makes the audit necessary for the registry; 'No... without' makes containment necessary for the audit; and 'prerequisite to' makes the commission necessary for containment. Linking these yields: Export → Registry → Audit → Containment → Commission.

Step-by-Step Solution

1
Translate the first rule involving 'only if'.
Exporting crops → Maintaining registry
The indicator 'only if' introduces a necessary condition. Thus, exporting is the sufficient condition that guarantees a registry is maintained.
2
Translate the second rule involving 'requires'.
Maintaining registry → Passing audit
The word 'requires' introduces a necessary condition. Therefore, maintaining the registry guarantees that the audit has been passed.
3
Translate the third rule involving 'No... without'.
Passing audit → Implementing containment
The phrase 'No X without Y' means Y is necessary for X. Passing the audit is sufficient to know that containment protocols are implemented.
4
Translate the fourth rule involving 'is prerequisite to'.
Implementing containment → Establishing commission
A 'prerequisite' is a necessary condition that must occur first. Therefore, implementing containment protocols guarantees that a commission has been established.
5
Synthesize the individual statements into a single deductive chain.
Exporting crops → Maintaining registry → Passing audit → Implementing containment → Establishing commission
By linking the shared sufficient and necessary conditions from each translated rule, an unbroken sequence is formed.

Key Concept

Translating and chaining conditional statements using varied indicators (only if, requires, no...without, prerequisite to).
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Topics

Diagramming Conditional Statements

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