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Difficulty: HardSyllogism and Categorical Propositions

Read the given statements and candidate conclusions carefully. Assume the statements are true even if they seem at variance with commonly known facts.

Statements:
1. Some decentralized protocols are encrypted ledgers.
2. All encrypted ledgers are immutable records.
3. All completely unhackable networks are encrypted ledgers.

Conclusions:
I. Some decentralized protocols are immutable records.
II. Some completely unhackable networks are encrypted ledgers.
III. All completely unhackable networks are immutable records.

Based on the rules of formal logic, which of the conclusions logically follow(s) from the given statements?

  1. A
    Only conclusions I and II follow
  2. Only conclusions I and III followAnswer
  3. C
    Only conclusion III follows
  4. D
    All conclusions I, II, and III follow

Answer

The correct answer is the option stating that only conclusions I and III follow.
Conclusion I is valid because the intersection of decentralized protocols and encrypted ledgers must fall entirely within the set of immutable records. Conclusion III is valid through a transitive chain: since all completely unhackable networks are encrypted ledgers, and all encrypted ledgers are immutable records, it logically follows that all completely unhackable networks are immutable records.

Step-by-Step Solution

1
Analyze Statements 1 and 2 to evaluate Conclusion I.
Since some decentralized protocols are encrypted ledgers, and all encrypted ledgers are immutable records, the intersecting portion must be immutable records.
This confirms Conclusion I ('Some decentralized protocols are immutable records') is logically valid.
2
Analyze Statement 3 to evaluate Conclusion II.
Statement 3 is a universal affirmative ('All C are E'). Conclusion II is a particular affirmative ('Some C are E'). In formal logic, universal statements do not guarantee the physical existence of their subjects.
Deriving a 'Some' conclusion solely from an 'All' premise commits the existential fallacy. Without a premise establishing their existence, Conclusion II is logically invalid.
3
Analyze Statements 2 and 3 to evaluate Conclusion III.
All completely unhackable networks are encrypted ledgers, and all encrypted ledgers are immutable records. Therefore, by the transitive property, all completely unhackable networks are immutable records.
This confirms Conclusion III is logically valid.

Key Concept

Syllogism and Categorical Propositions - Transitive Deductions and Existential Import
Estimated Time:2m 0s
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Topics

Syllogism and Categorical Propositions

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