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Zorluk: ZorSyllogism and Categorical Propositions

Read the given statements and candidate conclusions carefully.

Statements:
1. All cybersecurity analysts are system architects.
2. No system architect is a vulnerable network.
3. All vulnerable networks are high-risk assets.

Conclusions:
I. No cybersecurity analyst is a vulnerable network.
II. Some high-risk assets are not system architects.

Assuming that the given statements are true even if they appear at variance from commonly known facts, which of the candidate conclusions logically follow(s) from the statements under standard modern categorical logic (without assuming existential import for universal premises)?

  1. Only conclusion I followsCevap
  2. B
    Only conclusion II follows
  3. C
    Both conclusion I and conclusion II follow
  4. D
    Neither conclusion I nor conclusion II follows

Cevap

Only conclusion I follows.
The correct option identifies that only the first conclusion logically follows. Cybersecurity analysts are entirely contained within system architects, and no system architect overlaps with vulnerable networks. Hence, no cybersecurity analyst can be a vulnerable network. The second conclusion attempts to infer a particular relationship ('Some...') purely from universal statements, which constitutes an existential fallacy.

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1
Represent the statements using formal categorical logic propositions.
Statement 1 (A-type): All C are S (C⊆SC \subseteq S). Statement 2 (E-type): No S is V (S∩V=∅S \cap V = \emptyset). Statement 3 (A-type): All V are H (V⊆HV \subseteq H).
Converting verbal statements into set notation allows formal validation of conclusions.
2
Evaluate Conclusion I: 'No cybersecurity analyst is a vulnerable network' (C∩V=∅C \cap V = \emptyset).
Since C⊆SC \subseteq S and S∩V=∅S \cap V = \emptyset, any element in CC must also be in SS, and no element in SS can be in VV. Therefore, C∩V=∅C \cap V = \emptyset holds universally and unconditionally.
A subset of a set disjoint from another set must also be disjoint from that set.
3
Evaluate Conclusion II: 'Some high-risk assets are not system architects' (Particular Negative, O-type).
Deriving a particular statement ('Some...') from purely universal premises ('All...', 'No...') requires assuming existential import (that the set of vulnerable networks is non-empty). Without an explicit existential premise, drawing a particular conclusion from universal statements is an existential fallacy in modern Boolean categorical logic.
Universal statements do not guarantee the existence of members in modern formal logic.

Anahtar Kavram

Categorical Syllogism and Existential Fallacy
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Konular

Syllogism and Categorical Propositions

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