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Difficulty: MediumQuantifier Logic (Some, Most, All)

Consider the following premises: Most corporate lawyers at the firm hold advanced degrees in finance, and most corporate lawyers at the firm have handled international mergers. Based on these premises, it must be logically true that at least some individuals who have handled international mergers hold advanced degrees in finance.

Answer: Answer

Answer

True
The statement presents a valid logical deduction. When two 'most' statements share the same sufficient condition (the same subject group, which is corporate lawyers), their necessary conditions must overlap. If out of a group of 100100 lawyers, at least 5151 have finance degrees and at least 5151 have handled international mergers, there must be at least 22 lawyers with both traits. Thus, it must be true that at least some people who handled international mergers have finance degrees.

Step-by-Step Solution

1
Identify the base group and the associated quantifiers in the premises.
Base group: Corporate lawyers at the firm. Quantifiers: 'Most' (meaning strictly greater than 50%50\%).
To formalize the logical structure of the premises.
2
Translate the premises into formal logic.
Premise 1: Most A (corporate lawyers) are B (hold finance degrees). Premise 2: Most A (corporate lawyers) are C (have handled international mergers).
To clearly see the relationships between the groups.
3
Evaluate the necessary overlap between the two subsets.
Since both subsets (B and C) comprise more than 50%50\% of the total group A, they must overlap by at least one member. Thus, at least some A are both B and C.
To determine what mathematically must be true when two majorities are taken from the exact same finite set.
4
Analyze the conclusion given in the statement.
The conclusion states that 'some C are B'. Since we proved that there is an overlap (some A are both B and C), it logically follows that some C are B.
To compare the logically required overlap with the statement's conclusion.

Key Concept

Quantifier Overlap (Two 'Most' statements about the same subject)
Estimated Time:1m 0s
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Topics

Quantifier Logic (Some, Most, All)

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