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Difficulty: Very hardMust Be True / Most Strongly Supported

Biogeneticists have established the following regulatory parameters for synthetic genomes: All Class 3 synthetic genomes contain the zeta-promoter. Any genome containing the zeta-promoter requires continuous telomerase expression unless it lacks the chi-repressor. Furthermore, any genome that requires continuous telomerase expression exhibits rapid senescence when deprived of nutrient Q. However, no genome that lacks the chi-repressor is capable of synthesizing nutrient Q autonomously. Lastly, all Class 3 synthetic genomes developed at the Apex Institute are capable of synthesizing nutrient Q autonomously.

Evaluate the logical validity of the following statement: Any Class 3 synthetic genome developed at the Apex Institute exhibits rapid senescence when deprived of nutrient Q.

Answer: Answer

Answer

The statement evaluates to True because it is a logically guaranteed deduction from the provided conditional premises.
The conclusion rigorously follows from the premises. A Class 3 genome developed at Apex is capable of synthesizing nutrient Q. According to the fourth premise, lacking the chi-repressor prevents synthesizing nutrient Q. Thus, an Apex genome cannot lack the chi-repressor. Since all Class 3 genomes contain the zeta-promoter (premise 1), the Apex genome has the zeta-promoter. Because it has the zeta-promoter and does not lack the chi-repressor, the 'unless' exception fails, forcing it to require continuous telomerase expression (premise 2). Finally, requiring continuous telomerase expression guarantees rapid senescence when deprived of nutrient Q (premise 3).

Step-by-Step Solution

1
Formalize the foundational premises about genome properties.
1. Class 3 → zeta-promoter. 2. (zeta-promoter AND NOT lacking chi-repressor) → requires telomerase. 3. requires telomerase → rapid senescence without Q.
Mapping conditional relationships accurately is necessary to track the cascading constraints. 'Unless' introduces a necessary condition for avoiding the outcome.
2
Formalize the premises concerning the Apex Institute.
4. lacks chi-repressor → CANNOT synthesize Q. 5. Class 3 at Apex → CAN synthesize Q.
Isolating the characteristics of the specific subject (Class 3 at Apex) allows us to test the target statement.
3
Combine the premises to deduce the properties of Apex genomes.
A Class 3 genome at Apex CAN synthesize Q. Taking the contrapositive of premise 4 (CAN synthesize Q → DOES NOT lack chi-repressor), we deduce the genome does not lack the chi-repressor.
Applying contrapositives is required to connect the capabilities of the Apex genome back to the main regulatory parameters.
4
Complete the conditional chain to reach the final outcome.
The Apex genome is Class 3 (has zeta-promoter) and does NOT lack the chi-repressor. Therefore, it requires continuous telomerase expression, meaning it will exhibit rapid senescence without Q.
This confirms the statement perfectly matches the logical outcome of the premises.

Key Concept

Formal Logic: Conditional Chains, Contrapositives, and the 'Unless' Operator
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Topics

Must Be True / Most Strongly Supported

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