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Difficulty: MediumSyllogism and Categorical Propositions

Consider the following statements regarding modern smart-city infrastructure:
1. All autonomous vehicles are sensor-equipped machines.
2. No sensor-equipped machines are completely unpredictable systems.
3. Some completely unpredictable systems are weather phenomena.

Which of the following candidate conclusions logically follow from the given statements? Select all that apply.

  1. No autonomous vehicles are completely unpredictable systems.Answer
  2. Some weather phenomena are not sensor-equipped machines.Answer
  3. C
    All sensor-equipped machines are autonomous vehicles.
  4. D
    Some autonomous vehicles are weather phenomena.

Answer

The logically valid conclusions are: 'No autonomous vehicles are completely unpredictable systems' and 'Some weather phenomena are not sensor-equipped machines'.
The first valid conclusion correctly deduces that if the set of autonomous vehicles is entirely contained within the set of sensor-equipped machines, and the set of sensor-equipped machines is completely separate from the set of unpredictable systems, then autonomous vehicles must also be completely separate from unpredictable systems. The second valid conclusion correctly notes that since a portion of weather phenomena overlaps with unpredictable systems, and unpredictable systems are completely separate from sensor-equipped machines, that overlapping portion of weather phenomena cannot be sensor-equipped machines.

Step-by-Step Solution

1
Analyze the relationship between autonomous vehicles, sensor-equipped machines, and unpredictable systems.
Since every autonomous vehicle is a sensor-equipped machine, and no sensor-equipped machine is an unpredictable system, it follows that no autonomous vehicle can be an unpredictable system.
Applying the logical deduction rule for universal affirmative and universal negative premises.
2
Analyze the relationship between weather phenomena, unpredictable systems, and sensor-equipped machines.
We know some unpredictable systems are weather phenomena. Since unpredictable systems cannot be sensor-equipped machines, the specific weather phenomena that are unpredictable systems also cannot be sensor-equipped machines.
Applying the logical deduction rule for particular affirmative and universal negative premises.
3
Evaluate the remaining candidate conclusions for logical validity.
The conclusion stating that all sensor-equipped machines are autonomous vehicles is an invalid conversion. The conclusion linking autonomous vehicles to weather phenomena is invalid because no direct relationship is established between them in the premises.
Conclusions must be definitively proven by the given statements without external assumptions.

Key Concept

Evaluating categorical propositions and identifying valid logical deductions using standard syllogism rules.
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Topics

Syllogism and Categorical Propositions

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