Match each set of cybersecurity defense protocols (1-4) with the logically valid deduction… — LSAT

Match each set of cybersecurity defense protocols (1-4) with the logically valid deduction that must follow from those protocols. Assume no other protocols exist.

Protocol Set 1: The system audit is triggered only if the auxiliary backup is activated. The server core is isolated whenever the auxiliary backup is activated.If the server core is not isolated, then the system audit is not triggered.
Protocol Set 2: The server core is isolated only if the diagnostic protocols do not run. The system audit is triggered whenever the diagnostic protocols do not run.If the system audit is not triggered, then the server core is not isolated.
Protocol Set 3: The diagnostic protocols run whenever the system audit is triggered. The server core is isolated only if the diagnostic protocols do not run.If the system audit is triggered, then the server core is not isolated.
Protocol Set 4: The server core is isolated whenever the auxiliary backup is not activated. The auxiliary backup is activated only if the system audit is triggered.If the system audit is not triggered, then the server core is isolated.

Answer

Protocol Set 1 pairs with 'If the server core is not isolated, then the system audit is not triggered.' Protocol Set 2 pairs with 'If the system audit is not triggered, then the server core is not isolated.' Protocol Set 3 pairs with 'If the system audit is triggered, then the server core is not isolated.' Protocol Set 4 pairs with 'If the system audit is not triggered, then the server core is isolated.'

Each protocol set forms a unique transitive chain connecting the system audit (

A

) and the server core (

C

). By accurately translating 'only if' (necessary) and 'whenever' (sufficient) statements into formal logic, and applying the contrapositive rule (if

X \rightarrow Y

, then

\sim Y \rightarrow \sim X

), each set yields exactly one mathematically valid deduction provided in the options.

Step-by-Step Solution

Translate Protocol Set 1 into formal logic and derive its valid inference.

Let

A

= Audit triggered,

B

= Backup activated,

C

= Core isolated. Premises:

A \rightarrow B

and

B \rightarrow C

. Chain:

A \rightarrow C

. Contrapositive:

\sim C \rightarrow \sim A

'Only if' indicates a necessary condition (placed after the arrow), and 'whenever' indicates a sufficient condition (placed before the arrow).

Translate Protocol Set 2 into formal logic and derive its valid inference.

Let

D

= Diagnostics run. Premises:

C \rightarrow \sim D

and

\sim D \rightarrow A

. Chain:

C \rightarrow A

. Contrapositive:

\sim A \rightarrow \sim C

Linking the common intermediate term (

\sim D

) directly yields a continuous deductive chain from

C

A

Translate Protocol Set 3 into formal logic, apply a contrapositive to link terms, and derive the inference.

Premises:

A \rightarrow D

and

C \rightarrow \sim D

. The contrapositive of the second premise is

D \rightarrow \sim C

. Chain:

A \rightarrow D \rightarrow \sim C

. Result:

A \rightarrow \sim C

The premises cannot be chained directly. Taking the contrapositive of the second premise aligns the terms so they can form a valid transitive sequence.

Translate Protocol Set 4 into formal logic, apply a contrapositive to link terms, and derive the inference.

Premises:

\sim B \rightarrow C

and

B \rightarrow A

. The contrapositive of the second premise is

\sim A \rightarrow \sim B

. Chain:

\sim A \rightarrow \sim B \rightarrow C

. Result:

\sim A \rightarrow C

Just as in step 3, rearranging the second premise via contrapositive creates the bridge needed to link the variables

A

and

C

Key Concept

Translating conditional language into formal logic, chaining transitive statements, and deriving logically equivalent contrapositives.

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