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Difficulty: MediumSyllogism and Categorical Propositions

Read the following premises carefully and determine which of the given conclusions logically follow(s), assuming the premises to be absolutely true even if they seem to be at variance with commonly known facts.

Premises:
1. All encryption algorithms are security protocols.
2. Some security protocols are vulnerable systems.
3. No vulnerable system is approved for military use.

Conclusions:
I. Some encryption algorithms are vulnerable systems.
II. Some security protocols are not approved for military use.
III. No encryption algorithm is approved for military use.

Which of the following options is correct?

  1. Only conclusion II followsAnswer
  2. B
    Only conclusions I and II follow
  3. C
    Only conclusions II and III follow
  4. D
    All conclusions I, II, and III follow

Answer

Only conclusion II logically follows from the given premises.
Based on the rules of categorical syllogism, Conclusion II correctly links a particular affirmative (Some S are V) with a universal negative (No V are A) to yield a valid particular negative deduction (Some S are not A). The other conclusions attempt to force connections that are not strictly guaranteed by the premises.

Step-by-Step Solution

1
Analyze Conclusion I using the premises.
Conclusion I is invalid.
Premise 1 states 'All encryption algorithms are security protocols' and Premise 2 states 'Some security protocols are vulnerable systems'. The middle term 'security protocols' is not distributed in a way that connects 'encryption algorithms' to 'vulnerable systems'. The vulnerable systems might be a completely different subset.
2
Analyze Conclusion II using the premises.
Conclusion II is valid.
Premise 2 states 'Some security protocols are vulnerable systems' and Premise 3 states 'No vulnerable system is approved for military use'. The specific subset of security protocols that are vulnerable cannot be approved for military use. Therefore, it is definitively true that some security protocols are not approved for military use.
3
Analyze Conclusion III using the premises.
Conclusion III is invalid.
Since we could not logically establish that any encryption algorithms are vulnerable systems (from Step 1), we cannot conclude that they share the negative condition of being excluded from military use. They might fall entirely into the non-vulnerable, safe category of security protocols.

Key Concept

Syllogistic logic involving universal affirmative, particular affirmative, and universal negative propositions, emphasizing the rules of the undistributed middle.
Estimated Time:1m 30s
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Topics

Syllogism and Categorical Propositions

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