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Difficulty: MediumSyllogism and Categorical Propositions

Read the following statements and candidate conclusions carefully.

Statements:
1. All urban planners are sustainability experts.
2. No sustainability experts are climate change deniers.
3. Some public administrators are urban planners.

Conclusions:
I. Some public administrators are sustainability experts.
II. No urban planners are climate change deniers.

Which of the following options is correct regarding the validity of the conclusions?

  1. A
    Only conclusion I follows
  2. B
    Only conclusion II follows
  3. Both conclusion I and conclusion II followAnswer
  4. D
    Neither conclusion I nor conclusion II follows

Answer

Both conclusion I and conclusion II follow.
The correct answer states that both conclusion I and conclusion II follow. Conclusion I is valid because the subset of public administrators who are urban planners are necessarily sustainability experts. Conclusion II is valid because urban planners are entirely contained within sustainability experts, which shares no overlap with climate change deniers.

Step-by-Step Solution

1
Analyze Conclusion I
Statement 3 establishes that 'Some public administrators are urban planners'. Statement 1 states that 'All urban planners are sustainability experts'. Combining these gives: the public administrators who are urban planners must also be sustainability experts. Hence, 'Some public administrators are sustainability experts' is a valid deduction.
Conversion of particular affirmative premises via a universal affirmative chain yields a valid particular affirmative conclusion.
2
Analyze Conclusion II
Statement 1 states 'All urban planners are sustainability experts' and Statement 2 states 'No sustainability experts are climate change deniers'. Since urban planners form a subset of sustainability experts, and no sustainability expert is a climate change denier, no urban planner can be a climate change denier either. Hence, 'No urban planners are climate change deniers' is a valid deduction.
Universal negative relation transfers down to any subset of the subject class.
3
Synthesize final validity state
Since both Conclusion I and Conclusion II are logically necessary deductions, the option stating that both conclusions follow is correct.
Matching evaluated deductions with the candidate options.

Key Concept

Syllogistic Deductions and Categorical Propositions
Estimated Time:1m 0s
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Topics

Syllogism and Categorical Propositions

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