Examkin

Conditional Logic and Formal Deductions

11 soru

Tüm türler11Çoktan seçmeli7Doğru / Yanlış4
Soru 1Soru →

A marine conservation agency abides by the following guidelines regarding commercial oceanic operations: An oceanic research institute will approve a coastal zone for deep-sea mining only if the zone undergoes an ecological impact assessment. An ecological impact assessment is conducted whenever a designated marine habitat contains endangered coral species, unless the habitat is classified as a protected sanctuary. Furthermore, any coastal zone that undergoes an ecological impact assessment requires the implementation of continuous acoustic monitoring.

If the statements above are true, which of the following MUST also be true?

Cevabı ve açıklamayı göster

Cevap: A coastal zone cannot be approved for deep-sea mining without the implementation of continuous acoustic monitoring.

Cevap

A coastal zone cannot be approved for deep-sea mining without the implementation of continuous acoustic monitoring.
The passage establishes a chain of necessary conditions: approval for deep-sea mining requires an ecological impact assessment (Approval -> Assessment), and an ecological impact assessment requires continuous acoustic monitoring (Assessment -> Monitoring). Combining these transitive statements yields Approval -> Monitoring. The contrapositive of this deduction is that without continuous acoustic monitoring, a zone cannot receive approval for deep-sea mining.

Adım Adım Çözüm

1
Formalize the conditional statements provided in the passage.
Statement 1: Approval -> Assessment. Statement 2: Coral AND NOT Sanctuary -> Assessment. Statement 3: Assessment -> Monitoring.
Mapping the premises into logical notation clarifies valid deductions and prevents common fallacies.
2
Chain the conditional statements linking Approval, Assessment, and Monitoring.
Approval -> Assessment -> Monitoring. Thus, Approval -> Monitoring.
Transitive logic allows combining two nested conditional rules sharing a middle term (Assessment).
3
Take the contrapositive of the combined deduction.
NOT Monitoring -> NOT Approval.
A conditional statement is logically equivalent to its contrapositive, confirming that without monitoring, approval is impossible.

Anahtar Kavram

Conditional Logic and Formal Deductions
Soru 2Soru →

Under municipal transit regulations, a technology firm receives a commercial testing permit for autonomous trucks on public highways only if its navigation software achieves a Tier-1 safety certification. Achieving a Tier-1 safety certification requires completing at least 500,000 miles of simulated urban driving without a single critical system disengagement. Furthermore, unless a firm holds a commercial testing permit, it is forbidden from deploying autonomous vehicles during peak traffic hours.

If the statements above are true, which of the following must also be true?

Cevabı ve açıklamayı göster

Cevap: A technology firm that deploys autonomous vehicles on public highways during peak traffic hours has completed at least 500,000 miles of simulated urban driving without a critical system disengagement.

Cevap

A technology firm that deploys autonomous vehicles on public highways during peak traffic hours has completed at least 500,000 miles of simulated urban driving without a critical system disengagement.
The passage establishes a chain of necessary conditions: to deploy during peak traffic hours, a firm must hold a commercial testing permit; to have that permit, it must hold Tier-1 certification; and to achieve Tier-1 certification, it must complete 500,000 simulated miles without a critical disengagement. Therefore, any firm deploying vehicles during peak hours must have completed those 500,000 simulated miles.

Adım Adım Çözüm

1
Formalize the conditional statements given in the passage
Statement 1: Commercial Permit -> Tier-1 Certification. Statement 2: Tier-1 Certification -> 500,000 Simulated Miles without critical disengagement. Statement 3: Deploy Peak Hours -> Commercial Permit.
Translating natural language indicators ('only if', 'requires', 'unless') into formal logic clarifies necessary and sufficient conditions.
2
Chain the conditional statements together transitively
Deploy Peak Hours -> Commercial Permit -> Tier-1 Certification -> 500,000 Simulated Miles.
Because each condition is necessary for the preceding one, the entire chain must hold true.
3
Deduce the logically necessary conclusion
Deploying during peak traffic hours necessarily implies having completed at least 500,000 miles of simulated driving without a critical disengagement.
If the antecedent of the chain is true, all necessary conditions down the chain must also be true.

Anahtar Kavram

Transitive Chaining of Necessary Conditions
Soru 3Soru →

Consider the following international aerospace guidelines: A private satellite operator is granted a commercial orbital license only if its collision-avoidance system passes an automated telemetry audit. Passing an automated telemetry audit requires maintaining an active propulsion unit capable of immediate de-orbiting maneuvers.

Based on these guidelines, evaluate the following statement:
"If a private satellite operator maintains an active propulsion unit capable of immediate de-orbiting maneuvers, that operator is guaranteed to be granted a commercial orbital license."

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False. The statement commits a mistaken reversal fallacy because having an active propulsion unit is a necessary condition, not a sufficient condition, for receiving a commercial orbital license.
The evaluated statement is logically false because it commits a mistaken reversal. The rules state that receiving a license requires passing an audit, which in turn requires an active propulsion unit (License → Audit → Propulsion). Thus, maintaining a propulsion unit is merely a necessary prerequisite for obtaining a license, not a guarantee of receiving one.

Adım Adım Çözüm

1
Formalize the conditional premises from the passage
License → Telemetry Audit, and Telemetry Audit → Active Propulsion. Combining these yields the conditional chain: License → Telemetry Audit → Active Propulsion.
Identifying the directional relationships establishes which conditions are necessary versus sufficient.
2
Translate the evaluated statement into formal conditional logic
The statement asserts: Active Propulsion → License.
We must compare the claimed implication against the premises to test logical validity.
3
Evaluate the validity of the deduction
Claiming that Active Propulsion → License reverses the necessary condition chain (License → Active Propulsion). This is an invalid deduction known as a mistaken reversal.
Meeting a necessary requirement does not guarantee that the outcome itself will occur.

Anahtar Kavram

Mistaken Reversal in Conditional Reasoning Chains
Tahmini Süre:1m 30s
Soru 4Soru →

Under municipal heritage protection rules, a private conservation laboratory is granted an Elite Restoration License only if it maintains a continuous remote environmental monitoring system. A laboratory maintains a continuous remote environmental monitoring system whenever it operates an automated climate regulation system certified by the Standards Bureau. Furthermore, a laboratory requires an Elite Restoration License to be eligible to bid on state-funded artifact restoration contracts.

If the statements above are true, which of the following must also be true?

Cevabı ve açıklamayı göster

Cevap: A laboratory that is eligible to bid on state-funded artifact restoration contracts maintains a continuous remote environmental monitoring system.

Cevap

A laboratory that is eligible to bid on state-funded artifact restoration contracts maintains a continuous remote environmental monitoring system.
The passage establishes that eligibility to bid on state-funded contracts requires an Elite Restoration License, which in turn requires maintaining a continuous remote environmental monitoring system. Linking these two necessary conditions creates a valid transitive chain: Bidding Eligibility -> Elite Restoration License -> Remote Environmental Monitoring. Thus, any laboratory eligible to bid must maintain a continuous remote environmental monitoring system.

Adım Adım Çözüm

1
Formalize the conditional premises from the passage.
Premise 1: Bidding Eligibility -> Elite License. Premise 2: Elite License -> Remote Monitoring. Premise 3: Certified Climate System -> Remote Monitoring.
Translating natural language indicators ('only if', 'whenever', 'requires') into formal logic enables valid transitive deductions.
2
Chain the conditional statements involving Bidding Eligibility.
Bidding Eligibility -> Elite License -> Remote Monitoring.
Using hypothetical syllogism, if A requires B and B requires C, then A requires C.
3
Deduce the necessary inference.
Any laboratory eligible to bid on state-funded artifact restoration contracts must maintain a continuous remote environmental monitoring system.
This conclusion follows with formal logical certainty from the premise chain.

Anahtar Kavram

Conditional Logic Chaining and Valid Transitive Deductions
Soru 5Soru →

An enterprise software firm achieves ISO certification only if it implements end-to-end data encryption across all servers. Implementing end-to-end data encryption requires adopting a zero-trust network architecture. Furthermore, an enterprise software firm is permitted to bid on high-security municipal contracts only if it achieves ISO certification. Firm Apex is currently permitted to bid on high-security municipal contracts.

If the statements above are true, which of the following must also be true about Firm Apex?

Cevabı ve açıklamayı göster

Cevap: Firm Apex has adopted a zero-trust network architecture.

Cevap

Firm Apex has adopted a zero-trust network architecture.
The correct answer is derived from chaining the formal conditional rules provided: Permitted to Bid requires ISO Certification, which requires End-to-End Encryption, which requires Zero-Trust Architecture. Since Firm Apex is permitted to bid, it must satisfy all necessary prerequisites along the chain, including adopting a zero-trust network architecture.

Adım Adım Çözüm

1
Analyze the conditional premises in the passage
Premise 1: ISO Certification → End-to-End Encryption
Premise 2: End-to-End Encryption → Zero-Trust Architecture
Premise 3: Permitted to Bid → ISO Certification
Indicator words like 'only if' and 'requires' establish necessary conditions.
2
Chain the conditional statements transitively
Permitted to Bid → ISO Certification → End-to-End Encryption → Zero-Trust Architecture
Since each necessary condition links to the next, we can form a valid transitive deduction chain.
3
Apply the given fact about Firm Apex to the chain
Firm Apex is Permitted to Bid → Firm Apex MUST have adopted Zero-Trust Architecture
If the sufficient condition (Permitted to Bid) is true, all necessary conditions in the chain must also be true.

Anahtar Kavram

Transitive Chaining of Necessary Conditions
Soru 6Soru →

Passage: A scientific research journal will publish a manuscript only if the manuscript undergoes a double-blind peer review. A manuscript undergoes a double-blind peer review whenever it contains fully anonymized dataset references. Furthermore, a manuscript contains fully anonymized dataset references unless the authors submit a formal data-sharing exemption.

Based on the information provided, is the following statement True or False?
Statement: 'If authors do not submit a formal data-sharing exemption, their manuscript necessarily undergoes a double-blind peer review.'

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True
The statement is logically sound because combining the conditional rules yields a continuous valid chain: omitting a data-sharing exemption guarantees the inclusion of fully anonymized dataset references, which in turn guarantees that the manuscript undergoes a double-blind peer review.

Adım Adım Çözüm

1
Formalize the conditional premises from the passage.
Premise 1: Publish →\rightarrow Peer Review. Premise 2: Anonymized Datasets →\rightarrow Peer Review. Premise 3: ¬\neg Exemption →\rightarrow Anonymized Datasets.
Mapping the indicators ('only if', 'whenever', 'unless') into formal logic enables precise evaluation of validity.
2
Chain the relevant conditional statements to evaluate the target statement.
Combine Premise 3 and Premise 2: ¬\neg Exemption →\rightarrow Anonymized Datasets →\rightarrow Peer Review.
Since the conclusion of Premise 3 matches the condition of Premise 2, a valid transitive deduction is formed.
3
Compare the derived transitive deduction with the evaluated statement.
The statement asserts that ¬\neg Exemption →\rightarrow Peer Review, which perfectly matches the derived deduction.
The conclusion logically and necessarily follows from the provided premises.

Anahtar Kavram

Transitive Conditional Logic Chains
Soru 7Soru →

A financial technology firm will obtain an international trade license only if it completes a multi-jurisdictional compliance audit. Completing a multi-jurisdictional compliance audit requires establishing a dedicated risk-assessment division, unless the firm qualifies for a special regulatory waiver. However, no firm that handles decentralized digital asset transactions qualifies for a special regulatory waiver. Novabank handles decentralized digital asset transactions and has recently been granted an international trade license.

If the statements above are true, which of the following must also be true about Novabank?

Cevabı ve açıklamayı göster

Cevap: Novabank has established a dedicated risk-assessment division.

Cevap

Novabank has established a dedicated risk-assessment division.
The correct option is derived through a chain of formal conditional deductions. The stimulus establishes that obtaining an international trade license requires completing a multi-jurisdictional compliance audit. It further establishes that an audit requires a dedicated risk-assessment division unless a regulatory waiver applies. Finally, handling decentralized digital asset transactions rules out a regulatory waiver. Because Novabank possesses a trade license and handles digital assets, it must have completed the audit without a waiver, which strictly necessitates that Novabank established a dedicated risk-assessment division.

Adım Adım Çözüm

1
Analyze the conditional premises and given facts.
Premise 1: License → Audit. Premise 2: Audit → (Risk-Assessment Division OR Waiver). Premise 3: Digital Assets → NOT Waiver. Facts: Novabank has License AND Novabank has Digital Assets.
Deconstruct complex conditional statements into formal logical terms.
2
Deduce consequences of Novabank having an international trade license.
Since Novabank has a License, according to Premise 1, Novabank MUST have completed the multi-jurisdictional compliance audit.
Apply modus ponens on the necessary condition of licensing.
3
Deduce consequences of Novabank handling decentralized digital assets.
Since Novabank handles digital assets, according to Premise 3, Novabank CANNOT qualify for a regulatory waiver.
Determine the status of the exception clause.
4
Synthesize the intermediate deductions to reach the final valid inference.
Novabank completed the Audit (from Step 2). Audit requires Risk-Assessment Division UNLESS Waiver (from Premise 2). Since Waiver is false (from Step 3), Novabank MUST have established a dedicated risk-assessment division.
Combine disjunctive elimination with conditional requirement.

Anahtar Kavram

Chained Conditional Deductions and Disjunctive Elimination
Soru 8Soru →

Under current financial regulatory guidelines, a fintech enterprise is eligible for an expedited compliance audit only if it maintains a fully decentralized data architecture or operates under an approved regulatory sandbox exemption. An enterprise operates under an approved regulatory sandbox exemption only if its annual cross-border transaction volume does not exceed $50 million, unless it has secured a specialized risk-mitigation endorsement. Furthermore, any enterprise that maintains a centralized data architecture is strictly prohibited from obtaining a specialized risk-mitigation endorsement.

If a fintech enterprise maintains a centralized data architecture and processes $60 million in annual cross-border transactions, which of the following must be true based on the guidelines above?

Cevabı ve açıklamayı göster

Cevap: The enterprise is not eligible for an expedited compliance audit.

Cevap

The enterprise is not eligible for an expedited compliance audit.
The passage establishes three conditional statements: (1) Expedited Audit requires either Decentralized Architecture OR Sandbox Exemption. (2) If Volume > 50million,SandboxExemptionrequiresaSpecializedEndorsement.(3)CentralizedArchitecturepreventsobtainingaSpecializedEndorsement.ForafirmwithCentralizedArchitectureand50 million, Sandbox Exemption requires a Specialized Endorsement. (3) Centralized Architecture prevents obtaining a Specialized Endorsement. For a firm with Centralized Architecture and 60 million in volume: Centralized Architecture implies no Specialized Endorsement. Processing $60 million without a Specialized Endorsement means it cannot have a Sandbox Exemption. Having Centralized Architecture (no Decentralized Architecture) and no Sandbox Exemption means both necessary conditions for an Expedited Audit fail. Thus, it strictly follows that the enterprise is not eligible for an expedited compliance audit.

Adım Adım Çözüm

1
Formalize Premise 1 (Expedited Audit Eligibility)
Expedited Audit → Decentralized Architecture OR Sandbox Exemption. (Contrapositive: NOT Decentralized Architecture AND NOT Sandbox Exemption → NOT Expedited Audit)
Establishes the necessary conditions required for expedited audit eligibility.
2
Formalize Premise 2 (Sandbox Exemption Requirements)
Sandbox Exemption AND Volume > 50million→SpecializedEndorsement.(Contrapositive:NOTSpecializedEndorsementANDVolume>50 million → Specialized Endorsement. (Contrapositive: NOT Specialized Endorsement AND Volume > 50 million → NOT Sandbox Exemption)
Determines when a specialized risk-mitigation endorsement is necessary for maintaining sandbox status.
3
Formalize Premise 3 (Endorsement Restrictions)
Centralized Architecture → NOT Specialized Endorsement.
Links data architecture structure directly to endorsement eligibility.
4
Chain the deductions for a firm with Centralized Architecture and $60M Volume
1. Centralized Architecture → NOT Specialized Endorsement.
2. Volume > 50M(50M ( 60M) AND NOT Specialized Endorsement → NOT Sandbox Exemption.
3. Centralized Architecture (NOT Decentralized Architecture) AND NOT Sandbox Exemption → NOT Expedited Audit.
Applies contrapositive logic iteratively to derive the necessary conclusion.

Anahtar Kavram

Chained Conditional Logic and Contrapositive Deductions
Soru 9Soru →

A corporate compliance officer established the following rule for international transactions: Any transaction exceeding $100,000 requires prior approval from the risk assessment committee. Furthermore, whenever a transaction requires prior approval from the risk assessment committee, it must undergo a secondary audit by an independent auditor.

If an international transaction exceeded $150,000, which of the following must be true based on the compliance officer's rule?

Cevabı ve açıklamayı göster

Cevap: The transaction must undergo a secondary audit by an independent auditor.

Cevap

The transaction must undergo a secondary audit by an independent auditor.
The passage establishes a direct chain of conditional logic: a transaction exceeding 100,000requiresriskassessmentcommitteeapproval,andanytransactionrequiringsuchapprovalmustundergoasecondaryauditbyanindependentauditor.Because100,000 requires risk assessment committee approval, and any transaction requiring such approval must undergo a secondary audit by an independent auditor. Because 150,000 is greater than $100,000, both conditions in the chain are sequentially triggered, making it logically necessary that the transaction undergoes a secondary audit by an independent auditor.

Adım Adım Çözüm

1
Identify the given condition for the specific transaction
The transaction value is 150,000,whichsatisfiesthethresholdconditionof′exceeding150,000, which satisfies the threshold condition of 'exceeding 100,000'.
Establishing that the initial condition (150,000>150,000 > 100,000) is met triggers the first conditional rule.
2
Apply the first conditional rule
Since 150,000>150,000 > 100,000, the transaction requires prior approval from the risk assessment committee.
Rule 1 states: Transaction > $100,000 → Requires risk assessment committee approval.
3
Apply the second conditional rule in the chain
Because the transaction requires prior approval from the committee, it must undergo a secondary audit by an independent auditor.
Rule 2 states: Requires committee approval → Must undergo secondary audit by an independent auditor.

Anahtar Kavram

Hypothetical Syllogism (Chained Conditional Deductions)
Tahmini Süre:1m 0s
Soru 10Soru →

An agricultural board rule dictates that an orchard receives an organic certification only if it refrains from using synthetic pesticides for at least three consecutive years. Orchard Y has not used synthetic pesticides for the past four consecutive years.

Statement: Based on the rule above, Orchard Y must have received an organic certification.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

The statement is False. Meeting a necessary condition does not guarantee that a sufficient condition is met.
The statement is False because the agricultural board rule uses the phrase 'only if', establishing that avoiding synthetic pesticides is a necessary requirement for certification, not a guarantee of it. Satisfying a necessary condition does not prove that the final outcome must occur.

Adım Adım Çözüm

1
Identify the conditional relationship in the premise
Organic Certification → No synthetic pesticides for at least 3 years
The indicator 'only if' introduces a necessary condition.
2
Analyze the given fact about Orchard Y
Orchard Y satisfies the necessary condition (4 years without synthetic pesticides ≥ 3 years).
The premise states Orchard Y met the required timeframe.
3
Evaluate whether the conclusion logically follows
Inferring that Orchard Y must be certified is an invalid deduction (Mistaken Reversal).
Satisfying a necessary condition does not automatically trigger the outcome, as additional unstated conditions may be required.

Anahtar Kavram

Distinguishing Necessary Conditions from Sufficient Conditions
Soru 11Soru →

A biomedical research consortium establishes the following funding protocol: A clinical study receives financial backing only if the project team secures institutional ethics board certification and implements synthetic biomarker tracking. Securing institutional ethics board certification requires that the study protocol either undergoes double-blind peer review or obtains a regulatory exemption from the central health committee.

Consider the following assertion: If Study X was denied financial backing and did not obtain a regulatory exemption from the central health committee, then Study X must have failed to undergo double-blind peer review.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

The statement is False.
Evaluating the statement as False is correct because the rules state that financial backing requires ethics certification. The absence of financial backing does not imply that ethics certification was withheld or that double-blind peer review did not occur; Study X could have fulfilled the peer review requirement but missed financial backing due to another missing requirement (such as synthetic biomarker tracking).

Adım Adım Çözüm

1
Formalize the conditional premises from the protocol.
Premise 1: Financial Backing → (Ethics Certification AND Synthetic Biomarker Tracking).
Premise 2: Ethics Certification → (Double-Blind Peer Review OR Regulatory Exemption).
Establishing formal logic notation prevents misinterpreting necessary conditions as sufficient conditions.
2
Analyze the given facts about Study X.
Facts: ¬Financial Backing and ¬Regulatory Exemption.
Identify which components of the conditional statements are known to be true or false.
3
Test the validity of the deduction: ¬Financial Backing → ¬Double-Blind Peer Review.
From Premise 1, Financial Backing requires Ethics Certification. However, the absence of Financial Backing (¬Financial Backing) does not logically imply the absence of Ethics Certification (¬Ethics Certification).
Denying the antecedent (¬Financial Backing) yields no valid inference about the consequent (Ethics Certification).
4
Determine whether double-blind peer review must be false.
Since Ethics Certification could still be true, Double-Blind Peer Review could also be true. Therefore, it is not logically necessary that Study X failed to undergo double-blind peer review.
A statement is only logically necessary if it must be true in all possible valid scenarios consistent with the premises.

Anahtar Kavram

Conditional Logic: Distinguishing Necessary vs. Sufficient Conditions and Avoiding the Mistaken Negation Fallacy
Conditional Logic and Formal Deductions Alıştırma Soruları — GMAT | Examkin