Examkin

Soru

Zorluk: Çok zorSyllogism and Categorical Propositions

Consider the following three categorical statements:
1. No document is an index.
2. All indices are catalogs.
3. All catalogs are registers.

Which of the following conclusions logically follow from the given statements? (Select all that apply.)

  1. No index is a document.Cevap
  2. All indices are registers.Cevap
  3. C
    Some registers are indices.
  4. D
    No register is a document.

Cevap

The valid conclusions are 'No index is a document' and 'All indices are registers'.
The conclusions 'No index is a document' and 'All indices are registers' are strictly valid. The first is the direct logical conversion of the universal negative statement 'No document is an index'. The second is derived via transitive inclusion across the universal statements 'All indices are catalogs' and 'All catalogs are registers'.

Adım Adım Çözüm

1
Analyze Premise 1
Document ∩ Index = ∅
Universal negative premise 'No document is an index' means the sets of documents and indices are completely disjoint. Taking the converse gives 'No index is a document'.
2
Combine Premise 2 and Premise 3
Index ⊆ Catalog and Catalog ⊆ Register ⇒ Index ⊆ Register
Transitivity of subset inclusion ensures that all members of the index set are necessarily contained within the register set.
3
Evaluate existential import for particular conclusions
Particular statements cannot be inferred from purely universal premises without explicit existence assumptions.
In modern Boolean logic, universal statements ('All A are B') do not guarantee that category A has actual members. Thus, concluding 'Some registers are indices' commits the existential fallacy.
4
Evaluate scope of exclusion for Register and Document
Register ∩ Document is undetermined.
The fact that Index does not overlap with Document does not prevent non-index Registers from overlapping with Document.

Anahtar Kavram

Validation of Categorical Syllogisms and Avoidance of Existential Fallacy
Bu soruyu puanla

Konular

Syllogism and Categorical Propositions

Bu konudan daha fazla soru