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Under the revised corporate governance code, a board of directors can legally dismiss a chief executive officer only if the board achieves a supermajority vote. Furthermore, a supermajority vote is possible only when at least one independent director concurs with the board's executive directors. According to a recent audit, most companies in the Capstone Investment portfolio have boards consisting entirely of executive directors. However, any company in the Capstone Investment portfolio that has restated its quarterly earnings this year has legally dismissed its chief executive officer.

Which of the following logically follows from the information above?

  1. Most companies in the Capstone Investment portfolio have not restated their quarterly earnings this year.Cevap
  2. B
    Any company in the Capstone Investment portfolio that has an independent director on its board has legally dismissed its chief executive officer this year.
  3. C
    If a board of directors fails to achieve a supermajority vote, it cannot have an independent director who concurs with the executive directors.
  4. D
    None of the companies in the Capstone Investment portfolio are legally permitted to dismiss their chief executive officers.
  5. E
    Companies in the Capstone Investment portfolio that have restated their quarterly earnings this year did so because their executive directors disagreed with the chief executive officer.

Cevap

Most companies in the Capstone Investment portfolio have not restated their quarterly earnings this year.
The correct answer accurately combines the stimulus's formal logic chain with its central quantifier. The text establishes that restating earnings requires dismissing a CEO, and dismissing a CEO requires an independent director on the board. Therefore, any company that restates earnings must have an independent director (Restating Earnings -> Independent Director). Because we are told that 'most' Capstone Investment companies lack independent directors (their boards are 'entirely' executive), we can securely apply the contrapositive: most of these companies lack a necessary condition for restating earnings, and therefore, most have not restated their earnings.

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1
Map the conditional relationships provided in the first two sentences.
Dismissing a CEO requires a supermajority (Dismiss CEO -> Supermajority). A supermajority requires an independent director (Supermajority -> Independent Director).
Establishing the formal logic chain allows us to identify necessary conditions. Transitivity means: Dismiss CEO -> Independent Director.
2
Map the conditional relationship in the final sentence.
Restating earnings requires dismissing the CEO (Restate Earnings -> Dismiss CEO).
Connecting this to our previous chain gives us the full logical sequence: Restate Earnings -> Dismiss CEO -> Independent Director.
3
Apply the quantifier provided in the third sentence to the full conditional chain.
Most Capstone companies have boards entirely consisting of executive directors, meaning they lack an independent director. By contrapositive (~Independent Director -> ~Dismiss CEO -> ~Restate Earnings), most Capstone companies cannot have restated their earnings.
If a necessary condition (Independent Director) is missing for the majority of a group, then the sufficient conditions (Dismissing CEO, Restating Earnings) must also be absent for the majority of that group.

Anahtar Kavram

Chaining Conditional Statements with Quantifiers
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