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Zorluk: Çok zorParallel Quantifier Logic

Sociologist: Most successful grassroots campaigns rely on decentralized leadership. Furthermore, any organization relying on decentralized leadership must utilize digital communication platforms. Interestingly, most successful grassroots campaigns operate with minimal funding. Therefore, some initiatives operating with minimal funding must utilize digital communication platforms.

Which of the following arguments exhibit a pattern of reasoning that is logically parallel to that of the sociologist's argument? Select all that apply.

  1. Most atmospheric phenomena are driven by temperature gradients. All phenomena driven by temperature gradients require continuous energy input. Most atmospheric phenomena are observable from space. Thus, some events observable from space require continuous energy input.Cevap
  2. Most contemporary novels feature morally ambiguous protagonists. Every story featuring morally ambiguous protagonists challenges traditional narratives. Most contemporary novels receive mixed reviews from critics. Hence, some works receiving mixed reviews from critics challenge traditional narratives.Cevap
  3. C
    Most deep-sea organisms possess bioluminescent properties. All organisms possessing bioluminescent properties utilize luciferin. Some deep-sea organisms are discovered at depths below 4000 meters. Therefore, some organisms discovered at depths below 4000 meters utilize luciferin.
  4. D
    Most historical treaties were drafted during periods of economic instability. Only documents drafted during periods of economic instability are preserved in the national archives. Most historical treaties contain secret clauses. So, some documents containing secret clauses are preserved in the national archives.
  5. E
    Most technological revolutions cause temporary job displacement. All events causing temporary job displacement require robust social safety nets. Most technological revolutions ultimately improve living standards. Consequently, most events that ultimately improve living standards require robust social safety nets.

Cevap

The correct arguments are the one regarding atmospheric phenomena and the one regarding contemporary novels.
The correct arguments maintain the exact formal logic sequence of the stimulus: 'Most A are B, All B are C, Most A are D, Conclusion: Some D are C'. The 'atmospheric phenomena' and 'contemporary novels' examples replicate this valid intersection of two 'most' statements (which guarantees a 'some' overlap), combined correctly with a universal 'all' statement.

Adım Adım Çözüm

1
Deconstruct the formal logic of the stimulus.
The argument translates to: Most A are B; All B are C; Most A are D; Therefore, Some D are C.
Identifying the abstract algebraic structure of the premises and conclusion is essential for evaluating and finding parallel arguments.
2
Determine the logical validity of the stimulus.
The argument is valid. Combining 'Most A are B' and 'All B are C' mathematically implies 'Most A are C'. The overlap between 'Most A are C' and 'Most A are D' mathematically guarantees the conclusion 'Some D are C'.
Parallel reasoning requires matching not just the phrasing patterns, but the exact validity of the logical deductions.
3
Evaluate the choices for identical structural mappings.
The arguments regarding 'atmospheric phenomena' and 'contemporary novels' perfectly mirror the 'Most / All / Most -> Some' structure and are mathematically valid.
These choices maintain exact quantifier distribution and conclusion strength.
4
Eliminate choices with structural or quantifier flaws.
The remaining arguments shift 'Most' to 'Some', reverse the conditional relationship from 'All B are C' to 'Only B are C', or inappropriately escalate the conclusion to 'Most'.
Any deviation in quantifier scope or conditional direction breaks the logical parallelism.

Anahtar Kavram

Parallel Quantifier Logic and Set Overlaps
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Parallel Quantifier Logic

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