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Zorluk: KolaySyllogism and Categorical Propositions

Read the statements given below and the conclusions that follow. Assuming the given statements to be true even if they appear to contradict commonly known facts, determine which of the conclusions logically follow(s) from the statements.

Statements:
1. All delegates are representatives.
2. No representatives are diplomats.

Conclusions:
I. No delegates are diplomats.
II. Some diplomats are delegates.

Which of the following options is correct?

  1. Only conclusion I followsCevap
  2. B
    Only conclusion II follows
  3. C
    Both conclusion I and conclusion II follow
  4. D
    Neither conclusion I nor conclusion II follows

Cevap

Only conclusion I follows.
The statement establishing that all delegates belong to representatives, combined with the rule that no representatives are diplomats, logically guarantees that no delegate can be a diplomat. Therefore, the conclusion stating that no delegates are diplomats is strictly valid.

Adım Adım Çözüm

1
Analyze Premise 1 ('All delegates are representatives')
The set of Delegates (DD) is entirely contained inside the set of Representatives (RR), i.e., D⊆RD \subseteq R.
Universal affirmative statement establishes complete subset inclusion.
2
Analyze Premise 2 ('No representatives are diplomats')
The set of Representatives (RR) and the set of Diplomats (EE) are completely disjoint, i.e., R∩E=∅R \cap E = \emptyset.
Universal negative statement establishes complete set exclusion.
3
Evaluate Conclusion I ('No delegates are diplomats')
Since D⊆RD \subseteq R and R∩E=∅R \cap E = \emptyset, it follows that D∩E=∅D \cap E = \emptyset. Conclusion I is valid.
If a subset belongs to a set that has zero overlap with another set, the subset also has zero overlap with that set.
4
Evaluate Conclusion II ('Some diplomats are delegates')
Since D∩E=∅D \cap E = \emptyset, there can be no overlap between diplomats and delegates. Conclusion II is invalid.
A particular affirmative conclusion cannot hold between two mutually exclusive sets.

Anahtar Kavram

Categorical Syllogism (E-type universal negative derivation from A and E premises)
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Konular

Syllogism and Categorical Propositions

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