Question

Difficulty: HardMust Be True Questions

Consider the following premises regarding macroeconomic policy:

Any monetary policy framework that stabilizes inflation over a five-year period must rely on dynamic interest rate adjustments. Frameworks that rely on dynamic interest rate adjustments inherently fail to maintain the predictability of short-term lending rates. Furthermore, a monetary policy framework will not gain unanimous approval from the central banking committee unless it maintains the predictability of short-term lending rates.

Based on the information provided, it must be true that no monetary policy framework that stabilizes inflation over a five-year period will gain unanimous approval from the central banking committee.

Answer: Answer

Answer

True
The statement is logically true. By chaining the premises together (Stabilizes Inflation → Dynamic Adjustments → Fails Predictability), we establish that stabilizing inflation leads to failing to maintain predictability. The 'unless' rule dictates that Unanimous Approval → Maintains Predictability, which contraposes to Fails Predictability → No Unanimous Approval. Linking the entire chain proves that any framework stabilizing inflation will definitively not gain unanimous approval.

Step-by-Step Solution

1
Translate the first premise into a formal conditional statement.
Stabilizes Inflation (SI) → Dynamic Interest Rate Adjustments (DIRA)
The word 'Any' introduces a sufficient condition, and 'must rely' introduces a necessary condition.
2
Translate the second premise into a formal conditional statement.
DIRA → Fails to Maintain Predictability (~MP)
The statement indicates that relying on dynamic adjustments guarantees the failure to maintain predictability.
3
Translate the third premise into a formal conditional statement.
Unanimous Approval (UACB) → Maintains Predictability (MP)
The phrase 'not [A] unless [B]' translates logically to 'If [A], then [B]'. Here, gaining approval is the sufficient condition and maintaining predictability is the necessary condition.
4
Form the contrapositive of the third premise and chain all conditional statements.
Contrapositive: ~MP → ~UACB. Chain: SI → DIRA → ~MP → ~UACB
To connect the premises, the necessary condition of the second premise (~MP) must trigger the sufficient condition of the third premise. The contrapositive allows this connection.
5
Evaluate the final statement against the logical chain.
The final statement is valid and inherently True.
The logical chain simplifies to SI → ~UACB. The statement 'no monetary policy framework that stabilizes inflation... will gain unanimous approval' perfectly expresses this exact relationship.

Key Concept

Conditional logic chaining and translating 'unless' statements.
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