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Difficulty: MediumForming Contrapositives

According to the revised federal tax code, for a corporation to qualify for the green energy exemption, it is necessary that the corporation either sources at least half of its electricity from renewable methods or invests heavily in carbon sequestration research. The exemption was created to incentivize sustainable business practices across all industrial sectors without crippling economic growth.

Which one of the following statements can be logically inferred from the information provided above?

  1. If a corporation neither sources at least half of its electricity from renewable methods nor invests heavily in carbon sequestration research, it does not qualify for the green energy exemption.Answer
  2. B
    If a corporation sources at least half of its electricity from renewable methods, it will qualify for the green energy exemption.
  3. C
    If a corporation does not source at least half of its electricity from renewable methods, or if it does not invest heavily in carbon sequestration research, it cannot qualify for the green energy exemption.
  4. D
    If a corporation does not qualify for the green energy exemption, it must not source at least half of its electricity from renewable methods and must not invest heavily in carbon sequestration research.
  5. E
    A corporation that both sources at least half of its electricity from renewable methods and invests heavily in carbon sequestration research will definitely qualify for the green energy exemption.

Answer

The statement asserting that a corporation failing both the renewable sourcing requirement and the carbon sequestration investment requirement does not qualify for the green energy exemption.
The correct answer flawlessly applies the logical rule of contraposition and De Morgan's laws. The stimulus establishes that to qualify for the exemption, a corporation must meet at least one of two requirements (renewables OR sequestration). Therefore, if a corporation fails to meet both of these requirements, it has failed the necessary condition and logically cannot qualify for the exemption.

Step-by-Step Solution

1
Identify the conditional relationship in the stimulus.
Qualify for Exemption -> Source Renewables OR Invest in Sequestration.
The phrase 'it is necessary that... either... or' establishes the necessary conditions for qualifying.
2
Apply the rule for forming a contrapositive (negate and reverse) along with De Morgan's laws for compound conditionals.
NOT Source Renewables AND NOT Invest in Sequestration -> NOT Qualify for Exemption.
When a necessary condition contains an 'OR', negating it requires changing the 'OR' to an 'AND'. Failing both conditions guarantees the sufficient condition cannot occur.
3
Evaluate the options to find the one that matches this valid contrapositive.
The correct answer accurately states that failing both conditions ('neither... nor...') leads to not qualifying.
Only this option perfectly mirrors the logical deduction formed in step 2.

Key Concept

Forming Contrapositives with De Morgan's Laws
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Topics

Forming Contrapositives

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