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Zorluk: OrtaDiagramming Conditional Statements

According to the newly adopted Lunar Mining Treaty, a corporation will be granted a mining license only if it passes a comprehensive ecological impact review. Passing this ecological impact review requires that the corporation either has no prior orbital debris violations or has paid the standard remediation fee. Furthermore, any corporation that receives government subsidies is strictly prohibited from paying the standard remediation fee.

Which one of the following conclusions can be properly drawn from the rules of the treaty?

  1. A
    Any corporation that has paid the standard remediation fee and passed the ecological impact review will be granted a mining license.
  2. B
    If a corporation is granted a mining license, it must not have received government subsidies.
  3. C
    If a corporation is not granted a mining license, it must have failed the ecological impact review.
  4. If a corporation receives government subsidies and has a prior orbital debris violation, it will not be granted a mining license.Cevap
  5. E
    Most corporations that receive government subsidies will fail the ecological impact review.

Cevap

If a corporation receives government subsidies and has a prior orbital debris violation, it will not be granted a mining license.
The correct answer accurately synthesizes all three rules using valid contrapositives. If a corporation receives subsidies, it cannot pay the fee. If it also has a prior violation, it fails the clean record requirement. Because passing the review requires at least one of those two things (clean record OR fee), failing both means it fails the review. Finally, because passing the review is required for a mining license, failing the review guarantees it will not be granted a license.

Adım Adım Çözüm

1
Diagram the first conditional rule.
Mining License (ML) -> Pass Review (PR)
The phrase 'only if' introduces a necessary condition.
2
Diagram the second conditional rule.
Pass Review (PR) -> No Prior Violations (NPV) OR Paid Fee (PF)
The phrase 'requires that' introduces necessary conditions connected by 'or'.
3
Diagram the third conditional rule.
Government Subsidies (GS) -> NOT Paid Fee (~PF)
The rule strictly prohibits subsidized corporations from paying the fee.
4
Formulate the contrapositive of the second rule.
NOT No Prior Violations (~NPV) AND NOT Paid Fee (~PF) -> NOT Pass Review (~PR)
When negating an 'OR' statement, it becomes an 'AND' statement. If both necessary conditions fail, the sufficient condition must fail.
5
Chain the deductions together to test the scenario in the correct answer.
GS -> ~PF. A prior violation means ~NPV. Therefore, (GS AND ~NPV) triggers (~PF AND ~NPV). This triggers ~PR. From the first rule's contrapositive (~PR -> ~ML), this ultimately triggers ~ML.
Valid logical inferences require linking established sufficient conditions through to their ultimate necessary outcomes.

Anahtar Kavram

Chaining Conditional Statements and De Morgan's Laws
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Konular

Diagramming Conditional Statements

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