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

Premises: A technology firm requires all software engineers who work on cybersecurity infrastructure to complete an advanced cryptography certification. Marcus is a software engineer at the firm who has not completed the advanced cryptography certification.

Based solely on the premises above, evaluate the following statement:
Marcus does not work on cybersecurity infrastructure at the technology firm.

Answer: Answer

Answer

The statement is True.
The statement is True because it is the contrapositive of the rule stated in the premise. The premise dictates that working on cybersecurity infrastructure requires completing the cryptography certification. Therefore, lacking the certification guarantees that Marcus does not work on cybersecurity infrastructure.

Step-by-Step Solution

1
Identify the conditional relationship established in the premises.
If an engineer works on cybersecurity infrastructure, then they have completed the cryptography certification (Cybersecurity Infrastructure → Certification).
Establishing the formal conditional rule allows for valid logical deduction.
2
Apply the contrapositive rule of formal logic.
If an engineer has not completed the cryptography certification, then they do not work on cybersecurity infrastructure (NOT Certification → NOT Cybersecurity Infrastructure).
The contrapositive of any valid conditional statement is always logically equivalent and must be true.
3
Compare the contrapositive to the factual premise about Marcus.
Since Marcus has not completed the certification, it logically follows with absolute certainty that Marcus does not work on cybersecurity infrastructure.
Matching the given fact to the valid contrapositive guarantees the conclusion.

Key Concept

Valid Deduction via Contrapositive
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Topics

Identifying Must-Be-True Statements and Valid Deductions

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