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A corporation cannot be listed on the Apex Exchange unless it has undergone a comprehensive environmental audit. Only corporations that employ a dedicated sustainability officer can undergo a comprehensive environmental audit. No corporation that primarily manufactures synthetic plastics employs a dedicated sustainability officer. Furthermore, any corporation that qualifies for a municipal tax abatement either primarily manufactures synthetic plastics or fails to generate over ten million dollars in annual revenue.

Based on the information provided, any corporation listed on the Apex Exchange that qualifies for a municipal tax abatement fails to generate over ten million dollars in annual revenue.

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The statement is logically valid and therefore True.
The correct answer is True. By diagramming the premises, we derive the chain: Listed → Audit → Officer → Not Plastics. Therefore, any listed corporation cannot manufacture synthetic plastics. The stimulus also establishes: Abatement → Plastics OR Not Over 10M Revenue. If a corporation is both listed AND receives the abatement, it is automatically disqualified from the 'Plastics' option due to being listed. Therefore, by disjunctive syllogism, it must fulfill the only remaining option: failing to generate over ten million dollars in annual revenue. The statement is an undeniably valid deduction.

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1
Translate the first three premises into conditional logic chains.
Listed → Audit; Audit → Officer; Plastics → ~Officer.
Identifying the formal logic relationships is required to find connections between the terms.
2
Connect the individual conditions into a single transitive chain.
Listed → Audit → Officer → ~Plastics.
Combining the rules reveals the ultimate constraint placed on any corporation listed on the Apex Exchange.
3
Diagram the disjunctive premise concerning the tax abatement.
Abatement → (Plastics OR ~Over 10M Revenue).
The 'either...or' language establishes a necessary condition containing two distinct possibilities.
4
Apply the derived rules to the specific group mentioned in the statement: corporations that are both listed and receive the abatement.
Because they are listed, they must be ~Plastics. Because they receive the abatement, they must be (Plastics OR ~Over 10M Revenue).
To evaluate the statement, we must synthesize the conditions applying to this intersection of groups.
5
Utilize disjunctive syllogism to resolve the abatement condition.
Since the 'Plastics' option is impossible for listed corporations, the only remaining valid condition is '~Over 10M Revenue'.
When a necessary condition requires at least one of two options to be true, proving one false guarantees the other must be true.

Anahtar Kavram

Formal logic synthesis using transitive conditional chains, contrapositives, and disjunctive syllogism.
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Must Be True Questions

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