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Difficulty: MediumSyllogism and Categorical Propositions

If the statements 'All expressways are toll roads' and 'Some toll roads are privately maintained' are both true, then it necessarily follows that 'Some expressways are privately maintained'.

Answer: Answer

Answer

The statement is False because the logical deduction is invalid.
The proposed logical deduction is invalid because it fails to distribute the middle term in either premise, making the conclusion uncertain.

Step-by-Step Solution

1
Identify the logical structure and terms of the given premises.
The first premise is 'All E are T' (Universal Affirmative). The second premise is 'Some T are P' (Particular Affirmative). The proposed conclusion is 'Some E are P'.
Standardizing the categorical propositions helps in applying formal syllogistic rules or drawing Venn diagrams.
2
Analyze the distribution of the middle term ('toll roads' or 'T').
In the universal affirmative statement 'All E are T', the predicate 'T' is undistributed. In the particular affirmative statement 'Some T are P', the subject 'T' is also undistributed.
A valid categorical syllogism requires the middle term to be distributed in at least one of the premises.
3
Evaluate the validity of the conclusion based on the distribution.
Because the middle term is undistributed in both premises, no definitive relationship can be established between 'E' (expressways) and 'P' (privately maintained).
Without a distributed middle term, the specific toll roads that are expressways might not intersect at all with the specific toll roads that are privately maintained.

Key Concept

Validity of Syllogisms and the Fallacy of the Undistributed Middle
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Topics

Syllogism and Categorical Propositions

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