Question

Difficulty: MediumForming Contrapositives

Match each conditional cybersecurity rule from the corporate protocol manual on the left with its logically equivalent contrapositive on the right.

  • A contractor receives elevated system privileges only if they pass a comprehensive security audit.If a contractor does not pass a comprehensive security audit, they do not receive elevated system privileges.
  • Deploying the emergency containment protocol requires both authorization from the director and at least two active secondary servers.If director authorization is missing or there are fewer than two active secondary servers, the emergency containment protocol cannot be deployed.
  • The internal communications network will remain isolated unless the external threat neutralizes.If the internal communications network does not remain isolated, then the external threat must have neutralized.
  • An employee's device is flagged for immediate review if it connects to an unsecured network or downloads restricted software.If an employee's device is not flagged for immediate review, it must not have connected to an unsecured network and must not have downloaded restricted software.

Answer

The correct matches pair each original statement with its exact logical contrapositive by reversing the sufficient and necessary conditions, negating both, and properly applying De Morgan's laws to compound rules.
Each correct right-side item represents a logically valid deduction from the corresponding left-side item. The contrapositive is formed by universally reversing the direction of the conditional relationship and negating both sides. When terms include 'AND' or 'OR', De Morgan's laws correctly transform the operators during the negation process.

Step-by-Step Solution

1
Analyze the 'only if' statement regarding system privileges.
Matches with 'If a contractor does not pass a comprehensive security audit...'
'Only if' indicates a necessary condition (Privileges -> Audit). Reversing and negating yields: If not Audit, then not Privileges.
2
Analyze the compound 'requires both' statement regarding the containment protocol.
Matches with 'If director authorization is missing or there are fewer than two active secondary servers...'
The sufficient condition is deploying the protocol. The necessary condition is a conjunction (Director AND Servers). The contrapositive negates the conjunction into a disjunction (Not Director OR Not Servers).
3
Analyze the 'unless' statement regarding the communications network.
Matches with 'If the internal communications network does not remain isolated...'
'Unless' is translated as 'if not' (If not Neutralized -> Isolated). The contrapositive flips and negates this: If not Isolated -> Neutralized.
4
Analyze the compound 'if' statement regarding employee devices.
Matches with 'If an employee's device is not flagged for immediate review...'
The 'if' introduces a sufficient condition that is a disjunction (Unsecured OR Restricted -> Flagged). The contrapositive negates the disjunction into a conjunction: Not Flagged -> (Not Unsecured AND Not Restricted).

Key Concept

Forming Contrapositives and Applying De Morgan's Laws
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