Examkin

Question

Difficulty: MediumMust Be True Questions

All accredited zoological parks must maintain a full-time veterinary staff. Any facility that maintains a full-time veterinary staff allocates at least 20 percent of its operating budget to animal healthcare. Most facilities that allocate at least 20 percent of their operating budget to animal healthcare receive municipal grants.

Based strictly on the information above, the following statement must be true: Most accredited zoological parks receive municipal grants.

Answer: Answer

Answer

False
The statement is false because it commits a quantifier overreach error. While all accredited zoological parks allocate 20 percent to healthcare, they are merely a subset of such facilities. The fact that 'most' of these facilities receive grants does not guarantee that 'most' (or even any) of the zoological parks receive grants; they could logically belong to the minority that do not.

Step-by-Step Solution

1
Map the formal logic of the absolute premises.
Accredited zoological parks (AZP) → Full-time veterinary staff (FTV). FTV → Allocates 20% (A20).
Establishing the core conditional relationships is necessary to evaluate deductive inferences.
2
Combine the absolute conditional statements.
AZP → A20 (All accredited zoological parks allocate at least 20 percent of their budget).
Transitive chains allow connecting the first and last terms of absolute statements.
3
Evaluate the interaction between the absolute chain and the quantifier ('most').
We know AZP is a subset of A20. The premise states 'Most A20 → Municipal grants (MG)'. However, we cannot logically deduce that most of the AZP subset are MG.
Quantifiers like 'most' do not guarantee proportionate representation across all subsets of a group. The subgroup might exclusively occupy the minority portion of the larger group.

Key Concept

Quantifier Overreach in Formal Logic
Rate this question

Topics

Must Be True Questions

More questions from this topic