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Difficulty: MediumChaining Conditional Statements

According to a corporation's restructuring plan, if the board of directors approves the merger, then the marketing division will be downsized. Any downsizing of the marketing division requires that the public relations team be outsourced. Furthermore, the company will undergo a comprehensive financial audit only if the public relations team is not outsourced.

Based on the corporation's restructuring plan, which one of the following must be true?

  1. If the board of directors approves the merger, the company will not undergo a comprehensive financial audit.Answer
  2. B
    If the marketing division is downsized, it must be true that the board of directors approved the merger.
  3. C
    If the board of directors does not approve the merger, the public relations team will not be outsourced.
  4. D
    If the public relations team is not outsourced, then the company is guaranteed to undergo a comprehensive financial audit.
  5. E
    A comprehensive financial audit is typically avoided when a company decides to downsize its marketing division.

Answer

If the board of directors approves the merger, the company will not undergo a comprehensive financial audit.
The stimulus provides three conditional statements: (1) Merger Approved -> Marketing Downsized, (2) Marketing Downsized -> PR Outsourced, and (3) Financial Audit -> PR NOT Outsourced. By taking the contrapositive of the third statement, we get: PR Outsourced -> NO Financial Audit. Linking all these together creates a continuous chain: Merger Approved -> Marketing Downsized -> PR Outsourced -> NO Financial Audit. Therefore, if the merger is approved, the company absolutely cannot undergo a financial audit.

Step-by-Step Solution

1
Translate the first two premises into formal conditional logic.
Merger Approved -> Marketing Downsized; Marketing Downsized -> PR Outsourced.
To establish the initial chain of sufficient and necessary conditions.
2
Translate the third premise into formal conditional logic and find its contrapositive.
Audit -> PR NOT Outsourced. The contrapositive is: PR Outsourced -> NO Audit.
The phrase 'only if' introduces a necessary condition. Finding the contrapositive allows this premise to connect to the existing chain.
3
Chain all the conditional statements together.
Merger Approved -> Marketing Downsized -> PR Outsourced -> NO Audit.
The transitive property of conditional logic allows us to link shared necessary and sufficient conditions.
4
Evaluate the deduced chain to find a valid inference that matches an answer choice.
The chain directly supports the statement: If Merger Approved, then NO Audit.
In Must Be True questions, the correct answer is a direct, logically valid deduction from the provided premises.

Key Concept

Chaining Conditional Statements and Contrapositives
Estimated Time:1m 30s
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Topics

Chaining Conditional Statements

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