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Difficulty: MediumSyllogism and Categorical Propositions

Given the categorical premises: (1) 'No synthetic polymers are naturally occurring proteins' and (2) 'Some synthetic polymers are biodegradable materials', the conclusion 'No biodegradable materials are naturally occurring proteins' is logically valid.

Answer: Answer

Answer

The statement is False. The conclusion 'No biodegradable materials are naturally occurring proteins' is logically invalid because a particular premise cannot yield a universal conclusion.
The statement is False because deriving a universal negative statement from a combination of a universal negative premise and a particular affirmative premise violates syllogistic rules. The premises only support a particular negative deduction.

Step-by-Step Solution

1
Analyze the logical form of each premise.
Premise 1 is a Universal Negative (E-type: No S is N). Premise 2 is a Particular Affirmative (I-type: Some S is B).
Categorical syllogisms are evaluated by classifying propositions into A, E, I, or O types.
2
Apply syllogistic rules regarding particular premises.
The presence of particular premise 2 (I-type) dictates that any valid conclusion must be particular (O-type).
In formal logic, a universal conclusion cannot be validly derived if one of the premises is particular.
3
Compare the derived valid conclusion with the proposed conclusion.
The valid conclusion is 'Some B are not N' (O-type). The proposed conclusion is 'No B are N' (E-type), which over-generalizes to the entire set of biodegradable materials.
Inferring a universal negative claim when only a particular negative relation is proved violates standard logical rules.

Key Concept

Rules of Syllogistic Deduction and Fallacy of Particular Premise to Universal Conclusion
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Topics

Syllogism and Categorical Propositions

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