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Difficulty: HardParallel Quantifier Logic

Match each logical argument on the left to its logically parallel counterpart on the right. Both the distribution of quantifiers and the logical validity (or specific flaw) must perfectly align.

  • Most public parks feature playgrounds, and all places with playgrounds require regular maintenance; thus, most public parks require regular maintenance.Most modern novels contain romantic subplots, and any book with a romantic subplot sells well; thus, most modern novels sell well.
  • Some vintage cars are costly to insure, and most vintage cars need specialist mechanics; thus, most vehicles costly to insure need specialist mechanics.Some classical symphonies use a choir, and most classical symphonies have four movements; thus, most pieces that use a choir have four movements.
  • No high-speed trains operate on traditional tracks, and some freight routes utilize traditional tracks; thus, some freight routes are not high-speed trains.None of the local bakeries use artificial sweeteners, and some award-winning desserts use artificial sweeteners; thus, some award-winning desserts are not from local bakeries.
  • Most organic farms avoid synthetic pesticides, and most organic farms rely on crop rotation; thus, most farms that avoid synthetic pesticides rely on crop rotation.Most successful startup founders wake up early, and most successful startup founders read daily; thus, most early risers read daily.

Answer

The correct matches pair arguments sharing identical quantifier sequences and logical validity: the parks argument matches the novels argument (valid Most/All); the vintage cars argument matches the symphonies argument (flawed Some/Most); the trains argument matches the bakeries argument (valid No/Some); and the organic farms argument matches the startups argument (flawed Most/Most).
Each paired set features identical formal logic. The 'parks' and 'novels' arguments validly combine a 'Most' and 'All' premise. The 'vintage cars' and 'symphonies' arguments share an invalid deduction inferring a 'Most' relationship from a 'Some' and 'Most' premise. The 'high-speed trains' and 'local bakeries' arguments correctly deduce a 'Some... not' conclusion from a 'No' and 'Some' premise. The 'organic farms' and 'startup founders' arguments share the flaw of concluding 'Most' from two 'Most' premises.

Step-by-Step Solution

1
Map the formal logic structure of the first argument on the left.
The public parks argument follows: Most A are B. All B are C. Therefore, Most A are C. This is a valid deduction.
Establishing the baseline structure and validity is necessary before finding a parallel match.
2
Identify the parallel valid structure among the right-side options.
The modern novels argument mirrors this perfectly: Most A are B. All B are C. Therefore, Most A are C.
Parallel reasoning requires identical logical mapping, irrespective of subject matter.
3
Map the remaining structures on the left, paying close attention to logical flaws.
Vintage cars: Some A are B. Most A are C. Therefore, Most B are C (Invalid). Trains: No A are B. Some C are B. Therefore, Some C are not A (Valid). Organic farms: Most A are B. Most A are C. Therefore, Most B are C (Invalid).
Identifying the specific mechanism of flawed arguments is critical, as flawed structures must be paired with identically flawed structures.
4
Pair the remaining arguments based on identical structures and validity.
Trains (No/Some valid) matches bakeries. Vintage cars (Some/Most invalid) matches symphonies. Organic farms (Most/Most invalid) matches startups.
Complete the matching process by ensuring all quantifier variables and conclusions map 1-to-1.

Key Concept

Parallel Quantifier Logic
Estimated Time:2m 0s
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Parallel Quantifier Logic

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