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Difficulty: HardDiagramming Conditional Statements

In the context of international finance regulations, no corporate entity can successfully complete a hostile takeover without securing majority shareholder approval. Furthermore, completing such a takeover is possible only if the entity avoids antitrust litigation. Finally, avoiding antitrust litigation requires that the entity neither holds a monopoly in its primary market nor attempts to merge with its largest competitor.

If the statements above are true, which one of the following must also be true?

  1. A
    A corporate entity avoids antitrust litigation only if it successfully completes a hostile takeover.
  2. Any corporate entity that attempts to merge with its largest competitor cannot successfully complete a hostile takeover.Answer
  3. C
    If a corporate entity does not successfully complete a hostile takeover, it must either hold a monopoly in its primary market or have failed to secure majority shareholder approval.
  4. D
    Securing majority shareholder approval and avoiding antitrust litigation are sufficient conditions for a corporate entity to successfully complete a hostile takeover.
  5. E
    Most corporate entities that avoid antitrust litigation also secure majority shareholder approval during a hostile takeover.

Answer

The statement that any entity attempting to merge with its largest competitor cannot successfully complete a hostile takeover must be true.
This option correctly applies the contrapositive of the conditional chain established in the stimulus. The stimulus establishes that completing a takeover requires avoiding antitrust litigation (Takeover -> Avoid Litigation), and avoiding litigation requires NOT attempting to merge with the largest competitor (Avoid Litigation -> NOT Merge Largest). Chaining these together gives: Takeover -> NOT Merge Largest. The contrapositive is: Merge Largest -> NOT Takeover. This precisely matches the correct option.

Step-by-Step Solution

1
Translate the first two sentences into formal conditional logic.
Takeover -> Majority Approval AND Takeover -> Avoid Litigation.
The phrases 'no... without' and 'only if' introduce necessary conditions for the sufficient condition of successfully completing a hostile takeover.
2
Translate the final sentence into formal conditional logic.
Avoid Litigation -> NOT Monopoly AND NOT Merge Largest.
The word 'requires' introduces necessary conditions, and 'neither... nor' dictates that both conditions must be negated.
3
Chain the conditional statements together.
Takeover -> Avoid Litigation -> NOT Monopoly AND NOT Merge Largest.
Because 'Avoid Litigation' is necessary for 'Takeover' and sufficient for 'NOT Merge Largest', they form an unbroken deductive chain.
4
Form the contrapositive of the chained relationship.
Monopoly OR Merge Largest -> NOT Takeover.
Negating the necessary conditions (and flipping AND to OR) yields a sufficient condition that guarantees the takeover will not be completed.

Key Concept

Diagramming Conditional Statements and Contrapositives
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Topics

Diagramming Conditional Statements

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