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Difficulty: EasySyllogism and Categorical Propositions

Given the following statements:
1. All orbiters are satellites.
2. No satellites are landers.

Which of the following conclusions logically follow from the given statements?

  1. No orbiters are landers.Answer
  2. No landers are satellites.Answer
  3. C
    Some landers are orbiters.
  4. D
    All satellites are orbiters.

Answer

The conclusions stating 'No orbiters are landers' and 'No landers are satellites' logically follow from the given statements.
The statements establish that all orbiters are satellites and no satellites are landers. Consequently, orbiters and landers form entirely disjoint sets, making 'No orbiters are landers' a valid syllogistic deduction. In addition, the universal negative proposition 'No satellites are landers' converts directly into the valid statement 'No landers are satellites'.

Step-by-Step Solution

1
Analyze Premise 1 ('All orbiters are satellites') and Premise 2 ('No satellites are landers').
The set of orbiters is a subset of satellites, and the set of satellites has no elements in common with the set of landers.
Determining set inclusion and exclusion relationships.
2
Evaluate the relation between orbiters and landers.
Because orbiters are completely inside satellites and satellites are completely disjoint from landers, orbiters must also be completely disjoint from landers, yielding 'No orbiters are landers'.
Applying categorical syllogism rules (Celarent mode).
3
Evaluate immediate conversion of Premise 2.
'No satellites are landers' (E-type proposition) validly converts to 'No landers are satellites'.
Universal negative propositions undergo simple valid conversion.

Key Concept

Categorical Syllogisms and Immediate Inferences
Estimated Time:1m 0s
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Topics

Syllogism and Categorical Propositions

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