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Zorluk: OrtaIdentifying Sufficient Assumptions

Analyze each of the following logical arguments. Match each argument to the specific sufficient assumption that, if added to its premises, strictly and logically guarantees the truth of its conclusion.

  • The new software update improves battery life. Any software update that improves battery life is guaranteed to be widely downloaded. Therefore, the new software update will definitely increase the tech company's revenue.Any software update that is widely downloaded increases the revenue of the company that released it.
  • The mayor's zoning proposal will reduce urban sprawl. However, the city council will support a proposal only if it does not harm the local economy. Since the mayor's zoning proposal will not harm the local economy, it will surely be supported by the city council.The city council supports any proposal that does not harm the local economy.
  • A daily diet high in leafy greens provides a person with essential B-vitamins. We know that vitamin deficiencies often lead to chronic fatigue. Therefore, anyone who eats a diet high in leafy greens will not experience chronic fatigue.Anyone who consumes sufficient essential B-vitamins will not experience chronic fatigue.
  • Historically, civilizations that developed advanced writing systems experienced rapid technological growth. The newly discovered ancient civilization in the Valley of Lorn experienced rapid technological growth. Thus, the civilization in the Valley of Lorn must have developed an advanced writing system.Historically, the only civilizations to experience rapid technological growth were those that had developed advanced writing systems.

Cevap

Each argument requires a distinct formal logic assumption to guarantee its conclusion: linking a new term in the conclusion (Left 1 to Right 1), reversing a necessary condition to make it sufficient (Left 2 to Right 2), negating a condition to form a direct sufficient link (Left 3 to Right 3), and establishing a necessary condition for a historical outcome (Left 4 to Right 4).
Each matched assumption provides the exact logical bridge required to make the corresponding conclusion 100% valid, effectively transforming flawed or incomplete deductive arguments into airtight formal logic.

Adım Adım Çözüm

1
Analyze the first argument to identify the gap between the established premises and the main conclusion.
The premises prove the update will be 'widely downloaded,' but the conclusion claims it will 'increase revenue.'
Identifying the 'new' term in the conclusion reveals exactly what the sufficient assumption must connect.
2
Evaluate the conditional structure of the second argument regarding the mayor's proposal.
The premise gives 'Support -> Not Harm Economy'. The argument applies 'Not Harm Economy' to conclude 'Support'.
This is a classic flawed reversal. To make the argument logically valid, the relationship must be assumed in the other direction: 'Not Harm Economy -> Support'.
3
Identify the flawed reasoning in the third argument about leafy greens.
The premise states 'No Vitamins -> Fatigue'. The conclusion assumes 'Vitamins -> No Fatigue'.
This is a flawed negation. A sufficient assumption must bridge this by explicitly stating 'Vitamins -> No Fatigue'.
4
Diagram the formal logic in the fourth argument regarding the ancient civilization.
Premise: 'Writing -> Tech Growth'. Conclusion applied to Lorn: 'Tech Growth -> Writing'.
The argument improperly treats a sufficient condition as a necessary one. The assumption must state that writing is the 'only' way (a necessary condition) to achieve rapid technological growth.

Anahtar Kavram

Identifying Formal Logic Gaps and Sufficient Assumptions
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Konular

Identifying Sufficient Assumptions

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