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Difficulty: EasySyllogism and Categorical Propositions

Read the following statements carefully:
1. All archers are marksmen.
2. No marksmen are careless.

Based strictly on the given statements, which of the following conclusions logically follows?

  1. No archers are careless.Answer
  2. B
    Some archers are careless.
  3. C
    All marksmen are archers.
  4. D
    Some careless individuals are marksmen.

Answer

No archers are careless.
Because all archers are marksmen and no marksman is careless, the set of archers lies entirely inside the set of marksmen, which itself is completely disjoint from the set of careless people. Therefore, no archer can be careless.

Step-by-Step Solution

1
Analyze the first universal affirmative premise.
The set of 'Archers' is entirely contained within the set of 'Marksmen' (A⊂MA \subset M).
Establishes a subset relationship between archers and marksmen.
2
Analyze the second universal negative premise.
The set of 'Marksmen' and the set of 'Careless individuals' are completely disjoint (M∩C=∅M \cap C = \emptyset).
Establishes total mutual exclusion between marksmen and careless individuals.
3
Deduce the relationship between 'Archers' and 'Careless individuals'.
Since A⊂MA \subset M and M∩C=∅M \cap C = \emptyset, it follows that A∩C=∅A \cap C = \emptyset ('No archers are careless').
Applies standard transitive exclusion in categorical logic (EAE syllogism).

Key Concept

Syllogism and Categorical Propositions
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Topics

Syllogism and Categorical Propositions

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