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Zorluk: KolaySyllogism and Categorical Propositions

Read the following statements and candidate conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, determine which of the conclusions logically follow(s) from the given statements.

Statements:
1. All polymers are synthetic materials.
2. No synthetic materials are natural fibers.

Conclusions:
I. No polymers are natural fibers.
II. All natural fibers are polymers.

Which of the given conclusions logically follow(s) from the statements?

  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 conclusion stating that only conclusion I follows is correct. Because all polymers belong to the class of synthetic materials, and no synthetic material is a natural fiber, the class of polymers is entirely excluded from natural fibers. Hence, 'No polymers are natural fibers' is a direct and valid deduction.

Adım Adım Çözüm

1
Analyze Premise 1
Every element of set 'Polymers' is contained within set 'Synthetic Materials' (P⊆SP \subseteq S).
Universal affirmative premise establishing full inclusion.
2
Analyze Premise 2
Set 'Synthetic Materials' and set 'Natural Fibers' have no common elements (S∩N=∅S \cap N = \emptyset).
Universal negative premise establishing complete mutual exclusion.
3
Evaluate Conclusion I (No polymers are natural fibers)
Since P⊆SP \subseteq S and S∩N=∅S \cap N = \emptyset, it follows necessarily that P∩N=∅P \cap N = \emptyset.
A subset of a set disjoint from NN must also be disjoint from NN. Thus, Conclusion I is logically valid.
4
Evaluate Conclusion II (All natural fibers are polymers)
Since natural fibers share no elements with synthetic materials, they cannot share elements with polymers.
Conclusion II asserts an inclusion that directly contradicts the premise of mutual exclusion, so Conclusion II is invalid.

Anahtar Kavram

Categorical Syllogism (E-type deduction from A and E premises)
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Konular

Syllogism and Categorical Propositions

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