A compliance officer is mapping the consequences of a bank adopting the new Alpha cybersecurity protocol. The regulatory framework dictates the following:
1. If the Alpha protocol is implemented, the core server infrastructure must be upgraded.
2. Current vendor contracts can be maintained only if the core server infrastructure is not upgraded.
3. Unless the bank maintains its current vendor contracts, it will incur early termination penalties.
4. Any institution that incurs early termination penalties is subject to a flagged annual audit.
Arrange the logical steps in the correct deductive sequence to validly prove that implementing the Alpha protocol guarantees a flagged annual audit.
- 1Assume the initial sufficient condition: the bank implements the Alpha protocol.
- 2Deduce from the first rule that the core server infrastructure must be upgraded.
- 3Deduce from the contrapositive of the second rule that current vendor contracts cannot be maintained.
- 4Deduce from the third rule (translating 'unless' as 'if not') that early termination penalties will be incurred.
- 5Deduce from the fourth rule that the annual audit will be flagged.
Answer
The correct logical sequence starts by assuming the Alpha protocol is implemented, followed by deducing the server upgrade, then recognizing the broken vendor contracts via a contrapositive, leading to early termination penalties, and finally concluding with a flagged annual audit.
The correct sequence mirrors the logically valid transitive chain: Alpha -> Upgrade -> ~Maintain Contracts -> Penalties -> Flagged Audit. It properly accounts for the contrapositive of the 'only if' statement and correctly translates the 'unless' statement.
Step-by-Step Solution
Key Concept
Chaining conditional statements, utilizing contrapositives, and translating 'only if' and 'unless' statements into standard formal logic.