Examkin

Soru

Zorluk: Çok zorQuantifier Logic (Some, Most, All)

Consider the following premises about an ecosystem:

All migratory birds that nest in the Alpine Ridge rely on the silver-leaf willow for food.
Most migratory birds that nest in the Alpine Ridge have developed a resistance to the local avian flu.
Every bird that relies on the silver-leaf willow for food has a beak specially adapted for cracking seeds.
Most birds that have developed a resistance to the local avian flu carry a specific genetic marker, GM-42.

Based on these premises, it must be true that at least some birds with beaks specially adapted for cracking seeds carry the GM-42 genetic marker.

Cevap: Cevap

Cevap

The statement could be false, so it does not logically have to be true.
The statement is logically invalid because mathematically connecting 'Some A are B' with 'Most B are C' does not guarantee 'Some A are C'. The 'most' group of B could entirely exclude the 'some' group of A.

Adım Adım Çözüm

1
Deduce the relationship between Alpine Ridge birds and beak adaptations.
All Alpine Ridge birds rely on the willow, and all willow-reliant birds have adapted beaks. Therefore, all Alpine Ridge birds have adapted beaks (A → B, B → C means A → C).
This establishes a formal necessary condition for all Alpine Ridge birds, simplifying the first part of the stimulus.
2
Integrate the 'most' premise regarding Alpine Ridge birds and resistance.
Since most Alpine Ridge birds are resistant, and all Alpine Ridge birds have adapted beaks, we can validly deduce that at least some birds with adapted beaks are resistant (Some A are B).
This maps the relationship between the two target variables presented in the conclusion: adapted beaks and flu resistance.
3
Evaluate the final link between flu resistance and the GM-42 genetic marker.
The premises yield two isolated relationships: 'Some birds with adapted beaks are resistant' and 'Most resistant birds have the GM-42 marker'.
Isolating these formal relationships allows us to test the proposed conclusion strictly against the rules of quantifier logic.
4
Test the validity of combining 'Some X are Y' with 'Most Y are Z'.
There is no mathematical guarantee that the 'some' overlap in the first relationship shares any members with the 'most' majority in the second relationship. Thus, no valid deduction can be made.
This proves the target statement is a logical overreach and could be false.

Anahtar Kavram

Formal deductions from overlapping quantifiers (the invalidity of chaining 'Some' and 'Most')
Bu soruyu puanla

Konular

Quantifier Logic (Some, Most, All)

Bu konudan daha fazla soru