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Difficulty: HardDiagramming Conditional Statements

A maritime arbitration board relies on a strict set of regulations to determine the obligations and reimbursements for salvage operations.

You are given the initial premise: 'The cargo of the salvaged vessel is classified as containing hazardous materials.'
Your goal is to logically deduce the conclusion: 'The operation's costs will not be fully reimbursed by the state fund.'

Arrange the following regulatory rules in the exact logical sequence required to form an unbroken deductive chain from the given premise to the target conclusion.

  1. 1A cargo cannot be classified as containing hazardous materials unless the salvage operation is registered with the environmental protection agency.
  2. 2Unless an independent ecological auditor is deployed, a salvage operation cannot be registered with the environmental protection agency.
  3. 3A prerequisite for deploying an independent ecological auditor is the posting of a supplementary insurance bond.
  4. 4Any operation that posts a supplementary insurance bond is subject to a mandatory legal compliance audit.
  5. 5For an operation's costs to be fully reimbursed by the state fund, it must not be subject to a mandatory legal compliance audit.

Answer

The correct logical sequence translates the rules to form the chain: Hazardous Materials → EPA Registration → Auditor Deployed → Bond Posted → Mandatory Audit → Costs Not Reimbursed.
To build the deductive chain, each rule must be translated accurately into formal logic to connect the necessary condition of one rule to the sufficient condition of the next. The sequence begins with the premise 'Hazardous Materials' (HM). The rule 'Cannot be HM unless EPA' translates to HM → EPA. Next, 'Unless Auditor, cannot be EPA' translates to EPA → Auditor. Then, 'Prerequisite for Auditor is Bond' translates to Auditor → Bond. 'Any Bond is Audit' translates to Bond → Audit. Finally, 'For Reimbursed, must not Audit' translates to Reimbursed → Not Audit, whose contrapositive is Audit → Not Reimbursed. Chaining these yields: HM → EPA → Auditor → Bond → Audit → Not Reimbursed. Applying the premise HM, the conclusion Not Reimbursed validly follows in this exact sequence.

Step-by-Step Solution

1
Translate the rule containing the initial premise (Hazardous Materials).
rule_hm_epa translates to: Hazardous Materials → EPA Registration.
The phrase 'cannot be X unless Y' means if not Y, then not X (contrapositive: X → Y).
2
Find the rule triggered by EPA Registration.
rule_epa_iea translates to: EPA Registration → Auditor Deployed.
The phrase 'Unless X, cannot be Y' means if not X, then not Y (contrapositive: Y → X).
3
Find the rule triggered by Auditor Deployed.
rule_iea_sib translates to: Auditor Deployed → Bond Posted.
A 'prerequisite' is a necessary condition. If the auditor is deployed (sufficient condition met), the prerequisite must have been satisfied.
4
Find the rule triggered by Bond Posted.
rule_sib_lca translates to: Bond Posted → Mandatory Audit.
'Any X is Y' introduces a straightforward sufficient → necessary relationship.
5
Find the rule connecting Mandatory Audit to the final conclusion (Costs Not Reimbursed).
rule_lca_reimburse translates to: Costs Reimbursed → Not Audit. Contrapositive: Mandatory Audit → Costs Not Reimbursed.
Applying the contrapositive of this requirement completes the deductive chain to the target conclusion.

Key Concept

Conditional logic translation and deductive chaining
Estimated Time:2m 30s
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Topics

Diagramming Conditional Statements

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