Question

Difficulty: MediumIdentifying Must-Be-True Statements and Valid Deductions

At TechCorp, any department that implements Cloud System X must undergo a mandatory quarterly security audit. Every department undergoing a quarterly security audit is prohibited from using Legacy Software Y. Last year, the Financial Analytics division at TechCorp was authorized to use Legacy Software Y throughout all four quarters. If the statements above are true, which of the following must also be true regarding TechCorp last year?

  1. The Financial Analytics division did not implement Cloud System X during any quarter last year.Answer
  2. B
    The Financial Analytics division was the only department at TechCorp authorized to use Legacy Software Y last year.
  3. C
    Any department at TechCorp that did not implement Cloud System X last year was authorized to use Legacy Software Y.
  4. D
    The Financial Analytics division suffered no cybersecurity breaches while using Legacy Software Y last year.
  5. E
    If a department did not undergo a quarterly security audit last year, it was required to use Legacy Software Y.

Answer

The Financial Analytics division did not implement Cloud System X during any quarter last year.
The correct option stating that the Financial Analytics division did not implement Cloud System X during any quarter last year is logically necessary. From the premises, implementing Cloud System X requires a quarterly security audit, which in turn forbids using Legacy Software Y. By contrapositive logic, any department using Legacy Software Y cannot undergo a quarterly security audit and therefore cannot implement Cloud System X.

Step-by-Step Solution

1
Formalize premise 1
Implement Cloud System X → Quarterly Security Audit
Establishing the conditional rule linking System X to security audits.
2
Formalize premise 2
Quarterly Security Audit → NOT Authorized to use Legacy Software Y
Establishing the conditional rule linking security audits to Legacy Software Y prohibition.
3
Chain the premises together
Implement Cloud System X → Quarterly Security Audit → NOT Authorized for Legacy Software Y
Creating a unified conditional chain.
4
Form the contrapositive
Authorized to use Legacy Software Y → NOT Quarterly Security Audit → NOT Implement Cloud System X
Taking the logical contrapositive to deduce what follows from being authorized for Legacy Software Y.
5
Apply the facts about Financial Analytics
Financial Analytics used Legacy Software Y → Financial Analytics did NOT implement Cloud System X
Directly applying the contrapositive to the fact stated in the stimulus.

Key Concept

Conditional Logic Chains and Contrapositives
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