Inference and Deduction

215 soru

Soru 141Soru →

Under the newly drafted guidelines for experimental therapies, a novel neuroprotectant drug can be granted expedited regulatory review only if it demonstrates a statistically significant reduction in cellular degradation and does not trigger severe autoimmune responses in the test cohort.

Which one of the following logically follows from the guidelines described above?

Cevabı ve açıklamayı göster

Cevap: Any novel neuroprotectant drug that either fails to demonstrate a statistically significant reduction in cellular degradation or triggers severe autoimmune responses in the test cohort will be denied expedited regulatory review.

Cevap

The statement concluding that a drug will be denied expedited regulatory review if it either fails to demonstrate a statistically significant reduction in cellular degradation or triggers severe autoimmune responses in the test cohort.
The stimulus establishes a conditional rule where expedited review (the sufficient condition) requires two necessary conditions: demonstrating a significant reduction AND not triggering severe autoimmune responses. The valid contrapositive is formed by reversing the arrow and negating both sides. Applying De Morgan's laws, the negation of an 'AND' statement becomes an 'OR' statement, meaning the failure of EITHER necessary condition guarantees that the sufficient condition (expedited review) cannot occur.

Adım Adım Çözüm

1
Diagram the conditional premise provided in the stimulus.
Expedited Review → (Significant Reduction AND NOT Autoimmune Responses)
Identifying the sufficient condition (Expedited Review) and the necessary conditions (Significant Reduction, NO Autoimmune Responses) is required for formal logic deductions.
2
Form the contrapositive by reversing the conditional relationship and negating both sides.
NOT (Significant Reduction AND NOT Autoimmune Responses) → NOT Expedited Review
The contrapositive is the only logically valid deduction that can be drawn with certainty from a basic conditional statement.
3
Apply De Morgan's laws to simplify the negated necessary condition.
(NOT Significant Reduction OR Autoimmune Responses) → NOT Expedited Review
When negating a compound 'AND' statement, it becomes an 'OR' statement, and each individual term is negated (negating 'NOT Autoimmune Responses' becomes 'Autoimmune Responses').

Anahtar Kavram

Forming Contrapositives and Applying De Morgan's Laws
Soru 142Soru →

According to the latest meteorological frameworks, any atmospheric pressure system classified as a "hyper-cyclone" forms exclusively over ocean waters exceeding 28°C. A pressure system cannot form over such warm waters unless it is subject to severe Coriolis deflection. Furthermore, no weather system subject to severe Coriolis deflection maintains a perfectly symmetrical eyewall. Observations show that most hyper-cyclones cause significant coastal erosion upon landfall. Additionally, some pressure systems that maintain a perfectly symmetrical eyewall also cause significant coastal erosion upon landfall.

Which one of the following statements must be logically true based on the meteorological frameworks provided?

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Cevap: At least some weather systems that cause significant coastal erosion upon landfall do not maintain a perfectly symmetrical eyewall.

Cevap

At least some weather systems that cause significant coastal erosion upon landfall do not maintain a perfectly symmetrical eyewall.
The correct answer seamlessly combines the transitive conditional logic with the provided quantifier. The stimulus establishes a strict chain: if a system is a hyper-cyclone, it must form over waters exceeding 28°C; if it forms over such waters, it must be subject to severe Coriolis deflection; and if it is subject to severe Coriolis deflection, it cannot maintain a perfectly symmetrical eyewall. Transformed into a single rule, this means every hyper-cyclone lacks a perfectly symmetrical eyewall. The stimulus also states that 'most' hyper-cyclones cause significant coastal erosion. Because 'most' implies at least one, there exists at least one weather system that is a hyper-cyclone and causes significant coastal erosion. Since all hyper-cyclones lack a perfectly symmetrical eyewall, this specific system must also lack one. Therefore, it is mathematically guaranteed that at least some systems causing significant coastal erosion do not maintain a perfectly symmetrical eyewall.

Adım Adım Çözüm

1
Map the formal conditional statements provided in the stimulus.
Hyper-cyclone (HC) -> Waters > 28°C (W>28). W>28 -> Severe Coriolis Deflection (SCD). SCD -> NOT Symmetrical Eyewall (~PSE).
Establishing the logical baseline is required to find valid transitive inferences.
2
Connect the conditional statements to form a transitive chain.
HC -> W>28 -> SCD -> ~PSE. Therefore, HC -> ~PSE (All hyper-cyclones lack a perfectly symmetrical eyewall).
Transitive chaining simplifies multiple rules into a direct relationship between the first sufficient condition and the final necessary condition.
3
Map the quantifier statements regarding coastal erosion.
HC -most-> Significant Coastal Erosion (SCE). PSE -some-> SCE.
Quantifiers ('most', 'some') cannot be treated as strict conditionals but can interact with them to produce valid inferences.
4
Synthesize the transitive conditional chain with the quantifier statements.
Since 'most' HC cause SCE, at least one HC causes SCE. Since 'all' HC result in ~PSE, that specific HC causing erosion also lacks a perfectly symmetrical eyewall. Thus, SCE -some- ~PSE.
Combining a 'most' quantifier with an 'all' conditional guarantees that the qualities of the conditional necessarily apply to the 'most' group.

Anahtar Kavram

Synthesizing transitive conditional logic chains with non-absolute quantifiers (most/some) to derive provable deductions.
Soru 143Soru →

According to a recent ecological survey of the Veridian Basin:

Every tree species native to the Veridian Basin forms a symbiotic relationship with Mycena fungi. Any tree species that forms this symbiotic relationship requires highly acidic soil to thrive. Furthermore, most tree species currently cultivated in the newly established botanical gardens are native to the Veridian Basin. However, no tree species requiring highly acidic soil is tolerant of elevated soil salinity, even though at least some tree species tolerant of elevated soil salinity are successfully cultivated in the botanical gardens.

Based on the statements above, which of the following must be true? (Select all that apply.)

Geçerli olan tümünü seçin

Cevabı ve açıklamayı göster

Cevap: Most tree species cultivated in the newly established botanical gardens are not tolerant of elevated soil salinity.; At least some tree species cultivated in the newly established botanical gardens do not form a symbiotic relationship with Mycena fungi.

Cevap

The correct answers are the statements that 'most tree species cultivated in the newly established botanical gardens are not tolerant of elevated soil salinity' and 'at least some tree species cultivated in the newly established botanical gardens do not form a symbiotic relationship with Mycena fungi'.
Both correct statements are logically guaranteed by the text. The first correct statement is true because the 'most' quantifier carries through the conditional chain: if most garden trees are native, and all native trees ultimately cannot tolerate salinity, then most garden trees cannot tolerate salinity. The second correct statement is true because the text explicitly states some garden trees are tolerant of salinity. Taking the contrapositive of the established chain, any tree tolerant of salinity cannot require acidic soil, and therefore cannot form the Mycena symbiosis.

Adım Adım Çözüm

1
Map the universal conditional statements provided in the stimulus.
Native -> Mycena -> Acidic Soil -> NOT Saline Tolerant.
Tracking conditional chains allows us to see the absolute guarantees that flow from one characteristic to another.
2
Apply the 'Most' quantifier to the conditional chain.
Since MOST cultivated trees are Native, MOST cultivated trees trigger the entire chain: Mycena -> Acidic -> NOT Saline Tolerant.
When a subgroup defined by 'most' enters a conditional chain, the final necessary condition applies to 'most' of that subgroup.
3
Evaluate the 'Some' statement using the contrapositive of the chain.
SOME cultivated trees are Saline Tolerant. Saline Tolerant -> NOT Acidic Soil -> NOT Mycena -> NOT Native.
Applying the contrapositive to the subgroup of salinity-tolerant cultivated trees proves that they lack the prior necessary conditions in the chain.
4
Match deduced conclusions to the options.
The deduction from Step 2 matches the option regarding most cultivated trees lacking salinity tolerance. The deduction from Step 3 matches the option regarding some cultivated trees lacking the Mycena relationship.
Correct Must Be True options must be 100% deducible strictly from the mapped text.

Anahtar Kavram

Chaining Conditional Logic with Overlapping Quantifiers
Soru 144Soru →

Every residential development project approved by the City Council this year includes a minimum of 15% affordable housing units. Furthermore, most of the residential development projects approved by the City Council this year rely on municipal tax subsidies. However, the City Council strictly enforces a policy that no project relying on municipal tax subsidies can be located in the historic district.

Based on the information above, which one of the following statements must logically be true?

Cevabı ve açıklamayı göster

Cevap: At least some residential development projects that include a minimum of 15% affordable housing units are not located in the historic district.

Cevap

At least some residential development projects that include a minimum of 15% affordable housing units are not located in the historic district.
The stimulus establishes three facts: First, all approved projects have at least 15% affordable housing. Second, most approved projects rely on tax subsidies. This means there is a specific group of approved projects that feature both affordable housing and subsidies. Third, no project with subsidies is located in the historic district. By combining these facts, the projects that have both affordable housing and subsidies are prohibited from being in the historic district. Therefore, it is mathematically guaranteed that at least some projects with a minimum of 15% affordable housing are not in the historic district.

Adım Adım Çözüm

1
Map the formal logic rules established by the stimulus.
Rule 1: All Approved -> Affordable. Rule 2: Most Approved -> Subsidies. Rule 3: Subsidies -> NOT Historic.
Deconstructing the text into strict conditional and quantified relationships is required to find valid deductions safely.
2
Combine the 'All' and 'Most' statements sharing the same sufficient condition.
Because all approved projects are affordable, and most of them have subsidies, there is an intersection: at least some projects that are affordable also have subsidies.
When a group entirely possesses one trait and mostly possesses a second trait, the two traits must overlap on at least some members.
3
Apply the absolute conditional rule to the intersection group.
Since those overlapping projects have subsidies, Rule 3 dictates they cannot be in the historic district. Thus, some affordable projects are not in the historic district.
Connecting an absolute rule to an established subgroup yields a 100% provable conclusion.

Anahtar Kavram

Formal logic deductions involving conditional statements and overlapping quantifiers.
Soru 145Soru →

An autonomous vehicle's navigation system will pass the stringent Level 5 redundancy audit only if it incorporates dual-band LIDAR sensors, and operates with either a decentralized processing matrix or a quantum-encrypted communication link.

Which one of the following logically follows from the statement above?

Cevabı ve açıklamayı göster

Cevap: If an autonomous vehicle's navigation system does not incorporate dual-band LIDAR sensors, or if it operates with neither a decentralized processing matrix nor a quantum-encrypted communication link, then it will not pass the Level 5 redundancy audit.

Cevap

The statement expressing that if the system does not incorporate dual-band LIDAR sensors, or if it operates with neither a decentralized processing matrix nor a quantum-encrypted communication link, then it will not pass.
The stimulus establishes a conditional rule: Passing the audit requires LIDAR, plus at least one of two other features (Decentralized processing OR Quantum link). The logically valid contrapositive dictates that if you fail to meet these minimum requirements, you fail the audit. Failing the requirements means either lacking the mandatory LIDAR, OR lacking both of the alternative features. The correct answer precisely maps this logic.

Adım Adım Çözüm

1
Identify the sufficient and necessary conditions in the stimulus.
Sufficient: Passes the Level 5 redundancy audit. Necessary: Incorporates dual-band LIDAR AND (operates with decentralized processing OR quantum-encrypted link).
The phrase 'only if' introduces the necessary conditions for passing the audit.
2
Formulate the logical relationship.
Pass -> LIDAR AND (Decentralized OR Quantum)
This captures the compound nature of the necessary condition.
3
Apply De Morgan's laws to find the contrapositive.
Not [LIDAR AND (Decentralized OR Quantum)] -> Not Pass. This becomes: (Not LIDAR) OR Not (Decentralized OR Quantum) -> Not Pass. Further simplifying: (Not LIDAR) OR (Not Decentralized AND Not Quantum) -> Not Pass.
A valid logical inference from a conditional statement is its exact contrapositive. Negating an 'AND' creates an 'OR', and negating an 'OR' creates an 'AND'.
4
Match the derived contrapositive to the answer choices.
The correct choice translates the mathematical contrapositive into plain English: missing LIDAR, or missing both Decentralized and Quantum, guarantees failing the audit.
The correct answer must perfectly mirror the valid contrapositive structure.

Anahtar Kavram

Forming Complex Contrapositives with De Morgan's Laws
Soru 146Soru →

Any painting restored by Dr. Vance will be included in the upcoming exhibition. If a painting is included in the exhibition, the museum must insure it for over a million dollars. Furthermore, the museum will not insure any painting for over a million dollars unless it has been appraised by an independent panel. Any painting belonging to the Renaissance period has been appraised by an independent panel. Finally, no painting featuring religious motifs was restored by Dr. Vance.

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

Cevabı ve açıklamayı göster

Cevap: If a painting has not been appraised by an independent panel, it will not be included in the upcoming exhibition.

Cevap

If a painting has not been appraised by an independent panel, it will not be included in the upcoming exhibition.
The correct answer properly chains two conditional statements and takes the contrapositive. The stimulus states: 'Included in exhibition -> Insured >1M' and 'Insured >1M -> Appraised by independent panel'. Chaining these gives: 'Included in exhibition -> Appraised by independent panel'. The logical contrapositive of this new statement is: 'NOT Appraised by independent panel -> NOT Included in exhibition', which perfectly matches this option.

Adım Adım Çözüm

1
Translate the statements into formal conditional logic.
1: Restored by Vance -> Included in exhibition. 2: Included in exhibition -> Insured >1M. 3: Insured >1M -> Appraised by independent panel. 4: Renaissance -> Appraised by independent panel. 5: Religious motifs -> NOT Restored by Vance.
Mapping the logical relationships is necessary to see how the rules connect.
2
Identify connections between the conditional statements to form a chain.
Rules 1, 2, and 3 link together perfectly: Restored by Vance -> Included in exhibition -> Insured >1M -> Appraised by independent panel.
Chaining conditionals reveals deductive inferences that are not explicitly stated.
3
Derive the valid contrapositives of the logical chain.
The chain 'Included in exhibition -> Appraised by independent panel' yields the contrapositive: 'NOT Appraised by independent panel -> NOT Included in exhibition'.
Correct answers in Must Be True questions frequently rely on the contrapositive of a chained conditional statement.

Anahtar Kavram

Chaining Conditional Statements
Soru 147Soru →

Pair each set of operational spacecraft protocols with the logically valid deduction that can be correctly chained from its premises.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Öğeler

If the probe enters the atmosphere, the heat shield deploys. If the heat shield deploys, telemetry data is transmitted.
The probe enters the atmosphere only if the solar panels retract. Telemetry data is transmitted only if the solar panels do not retract.
Unless the primary engine fires, the orbit will not stabilize. Telemetry data is transmitted only if the orbit stabilizes.
If the backup battery engages, the primary engine fires. The orbit stabilizes only if the primary engine does not fire.

Eşleşmeler

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Cevap

Each premise set must be translated into formal if-then logic to locate the shared term. By applying contrapositives where necessary, you can form a continuous transitive chain (A -> B -> C) to reach the required conclusion.
The correct pairings successfully utilize formal logic rules, particularly the contrapositive, to link the sufficient condition of one premise to the necessary condition of the second, resulting in an unassailable deduction.

Adım Adım Çözüm

1
Translate each statement into formal conditional logic, paying close attention to indicator words like 'if', 'only if', and 'unless'.
You produce a set of logical relationships, such as A -> B and C -> Not B.
Standardizing the language allows you to see the logical flow without getting distracted by the narrative context.
2
Identify the shared variable between the two conditional statements.
You isolate the term that will act as the bridge in the deductive chain.
A chain can only be formed if the necessary condition of one statement matches the sufficient condition of another.
3
Apply the contrapositive to one of the statements if the shared variable has a mismatched polarity (e.g., B in one statement, Not B in the other).
The statements align cleanly (e.g., C -> Not B, and Not B -> Not A).
The contrapositive preserves the original truth value while rearranging the terms to enable transitive linking.
4
Follow the transitive property from the first sufficient condition to the final necessary condition.
You formulate the final valid deduction (e.g., C -> Not A).
This guarantees the final inference must logically be true based on the initial premises.

Anahtar Kavram

Chaining Conditional Statements
Soru 148Soru →

A municipal legal analyst is constructing a formal proof to demonstrate that if the city's Annual Arts Festival takes place this year, then the Mayor must not have signed the controversial Riverfront Zoning Act. The analyst relies on the following established municipal facts:

- The Mayor signs the Riverfront Zoning Act only if the Riverside Corporation initiates the condo project.
- The Riverside Corporation initiates the condo project only if they receive a property tax exemption.
- Any property tax exemption granted to developers requires the city to reduce its discretionary spending.
- Whenever the city reduces its discretionary spending, the Parks Maintenance Budget is eliminated.
- The Annual Arts Festival takes place only if the Parks Maintenance Budget is not eliminated.

Arrange the following intermediate deductions in the logically valid sequence that bridges the given premise 'The Annual Arts Festival is taking place' to the final conclusion 'The Mayor did not sign the Riverfront Zoning Act'.

Öğeleri doğru sıraya koymak için sürükleyin

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Cevap

The logically valid sequence begins with the occurrence of the festival and proceeds backwards through a chain of contrapositives: deducing the budget is intact, leading to no reduction in spending, meaning no tax exemption, resulting in no condo project, and finally proving the Mayor did not sign the Act.
The correct sequence forms a continuous chain of valid deductive inferences using the contrapositive of each conditional premise. Starting with the given fact (Festival), we apply Festival -> ~Eliminated, then ~Eliminated -> ~Reduced, then ~Reduced -> ~Exemption, then ~Exemption -> ~Project, and finally ~Project -> ~Mayor. Each step correctly identifies the logical relationship (sufficient vs. necessary) required to bridge the previous deduction to the next.

Adım Adım Çözüm

1
Identify the initial given fact and apply the first relevant conditional statement.
Deduce that the Parks Maintenance Budget remains intact.
The festival is taking place, and it taking place requires the budget to not be eliminated. Symbolically: Festival -> ~Eliminated.
2
Apply the derived fact (~Eliminated) to the next conditional statement in the chain.
Deduce that the city did not reduce its discretionary spending.
Reducing spending is sufficient for eliminating the budget (Reduced -> Eliminated). By the contrapositive (~Eliminated -> ~Reduced), spending was not reduced.
3
Continue the contrapositive chain using the absence of reduced spending.
Deduce that no property tax exemption was granted.
Exemptions require reduced spending (Exemption -> Reduced). By the contrapositive (~Reduced -> ~Exemption), no exemption was granted.
4
Apply the absence of the tax exemption to the condo project condition.
Deduce that the condo project is not initiated.
The project requires an exemption (Project -> Exemption). By the contrapositive (~Exemption -> ~Project), it is not initiated.
5
Apply the absence of the condo project to the final conditional statement.
Conclude that the Mayor did not sign the Act.
The Mayor signing requires the project to be initiated (Mayor -> Project). By the contrapositive (~Project -> ~Mayor), the Mayor did not sign the Act.

Anahtar Kavram

Chaining Conditional Statements via Contrapositives
Soru 149Soru →

According to the newly implemented botanical garden regulations, if a botanical specimen is classified as a delicate cultivar, it must be kept in the restricted conservatory. A specimen can be kept in the restricted conservatory only if it undergoes weekly pathogen screening. Furthermore, any specimen that undergoes weekly pathogen screening is exempt from the standard public exhibition rotation.

Based on the regulations above, which of the following must be true?

Cevabı ve açıklamayı göster

Cevap: If a botanical specimen is part of the standard public exhibition rotation, it is not classified as a delicate cultivar.

Cevap

If a botanical specimen is part of the standard public exhibition rotation, it is not classified as a delicate cultivar.
The premises create a continuous logical chain: being a delicate cultivar guarantees placement in the restricted conservatory, which guarantees pathogen screening, which guarantees exemption from the public exhibition rotation (Delicate Cultivar -> Not in Exhibition). The correct answer is the logical contrapositive of this final chain: if a specimen IS in the public exhibition rotation, it cannot be a delicate cultivar (In Exhibition -> Not a Delicate Cultivar).

Adım Adım Çözüm

1
Translate the rules into conditional statements.
1: Delicate Cultivar (DC) -> Restricted Conservatory (RC). 2: Restricted Conservatory (RC) -> Weekly Pathogen Screening (WPS). 3: Weekly Pathogen Screening (WPS) -> Not in Public Exhibition Rotation (~PER).
Formalizing the logic makes it easier to track the relationships, noting that 'only if' introduces a necessary condition.
2
Chain the conditional statements together.
DC -> RC -> WPS -> ~PER.
Since the necessary condition of each rule matches the sufficient condition of the next, they can be linked into a continuous chain.
3
Derive valid inferences and their contrapositives.
Valid chain inference: DC -> ~PER. Contrapositive: PER -> ~DC.
The correct answer to a Must Be True question involving formal logic is almost always the chained conclusion or its direct contrapositive.

Anahtar Kavram

Chaining Conditional Statements
Soru 150Soru →

A municipal planning board adheres to the following regulations for commercial developments:
- If a development is located in the waterfront zone, it must conduct an ecological impact study.
- Any development that conducts an ecological impact study is mandated to construct shoreline defenses.
- A development is granted a reduced property tax rate only if it is not mandated to construct shoreline defenses.
- Any development that receives a mayoral endorsement is granted a reduced property tax rate.

To validly deduce the conclusion 'If a development is located in the waterfront zone, it does not receive a mayoral endorsement,' arrange the following conditional deductions in the correct logical sequence of the transitive chain. Start with the initial trigger and end with the final deductive step.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct sequence connects the waterfront zone to the lack of mayoral endorsement through a transitive chain involving ecological studies, shoreline defenses, and property tax rates by applying two contrapositives.
The correct sequence builds a valid transitive logic chain. It begins with the initial premise (Waterfront -> Ecological Study), continues to the second premise (Ecological Study -> Shoreline Defenses), utilizes the contrapositive of the third premise (Reduced Tax Rate -> NO Shoreline Defenses becomes Shoreline Defenses -> NO Reduced Tax Rate), and finally utilizes the contrapositive of the fourth premise (Mayoral Endorsement -> Reduced Tax Rate becomes NO Reduced Tax Rate -> NO Mayoral Endorsement).

Adım Adım Çözüm

1
Identify the initial trigger from the required conclusion.
The chain must start with 'Waterfront zone'.
The conclusion we need to prove is 'Waterfront zone -> NO mayoral endorsement'.
2
Apply the first premise.
Waterfront zone -> Ecological impact study.
The rules explicitly state waterfront developments must conduct the study.
3
Chain the second premise.
Ecological impact study -> Shoreline defenses.
The rules explicitly state any development with a study must construct defenses.
4
Derive the contrapositive of the third premise.
Shoreline defenses -> NO reduced property tax rate.
The rule 'Reduced tax rate only if NO shoreline defenses' translates to (Reduced Tax Rate -> NO Shoreline Defenses). The contrapositive is (Shoreline Defenses -> NO Reduced Tax Rate).
5
Derive the contrapositive of the fourth premise.
NO reduced property tax rate -> NO mayoral endorsement.
The rule 'Mayoral endorsement -> Reduced tax rate' translates to (Mayoral Endorsement -> Reduced Tax Rate). The contrapositive is (NO Reduced Tax Rate -> NO Mayoral Endorsement).

Anahtar Kavram

Chaining Conditional Statements
Tahmini Süre:1m 30s
Soru 151Soru →

According to the newly ratified International Maritime Treaty, a sovereign vessel is permitted to navigate through the restricted ecological zone only if it possesses a valid ecological waiver or operates exclusively on electric power.

Which one of the following statements can be logically inferred from the treaty regulations above?

Cevabı ve açıklamayı göster

Cevap: Any sovereign vessel that neither possesses a valid ecological waiver nor operates exclusively on electric power is prohibited from navigating through the restricted ecological zone.

Cevap

The logically valid inference is that a vessel lacking both a valid ecological waiver and electric power cannot navigate the restricted zone.
The correct answer accurately applies De Morgan's laws to form a valid contrapositive. The stimulus dictates that permission to navigate requires at least one of two things: a waiver OR electric power. Therefore, if a vessel lacks BOTH (neither a waiver nor electric power), it has failed the necessary condition and must be prohibited from navigating.

Adım Adım Çözüm

1
Diagram the original conditional statement from the stimulus.
Permitted to Navigate -> (Possesses Waiver OR Operates on Electric Power)
The phrase 'only if' introduces a necessary condition. Because there are two ways to meet it, we use the logical 'OR'.
2
Form the contrapositive by reversing the conditions and negating both sides.
NOT (Possesses Waiver OR Operates on Electric Power) -> NOT Permitted to Navigate
A valid logical inference from a conditional statement is its exact contrapositive.
3
Apply De Morgan's laws to simplify the negated compound necessary condition.
(NOT Possesses Waiver AND NOT Operates on Electric Power) -> NOT Permitted to Navigate
Negating an 'OR' statement turns it into an 'AND' statement. In plain English, 'not A or B' becomes 'neither A nor B'.
4
Match the resulting logical statement to the correct answer choice.
The correct option states that any vessel that neither possesses a waiver nor operates on electric power is prohibited from navigating.
This choice perfectly aligns with the simplified contrapositive diagram.

Anahtar Kavram

Forming compound contrapositives using De Morgan's laws (negating 'OR' into 'AND').
Soru 152Soru →

If a tectonic plate subducts at an angle greater than 45 degrees, the resulting volcanic arc is invariably situated more than 200 kilometers from the corresponding oceanic trench. Furthermore, no volcanic arc situated more than 200 kilometers from a trench produces tholeiitic basalt exclusively. However, geological surveys have confirmed that most volcanic arcs within the Cenozoic Belt produce tholeiitic basalt exclusively.

Which one of the following statements can be properly inferred from the information above?

Cevabı ve açıklamayı göster

Cevap: Most volcanic arcs within the Cenozoic Belt are the result of tectonic plates subducting at an angle of 45 degrees or less.

Cevap

Most volcanic arcs within the Cenozoic Belt are the result of tectonic plates subducting at an angle of 45 degrees or less.
By chaining the conditional statements, we establish that subducting at an angle greater than 45 degrees guarantees the volcanic arc will not produce tholeiitic basalt exclusively. The logical contrapositive dictates that if an arc DOES produce tholeiitic basalt exclusively, its subduction angle must be 45 degrees or less. Since the text explicitly states that most Cenozoic Belt arcs produce this basalt exclusively, it logically guarantees that most of them formed at subduction angles of 45 degrees or less.

Adım Adım Çözüm

1
Identify and diagram the first conditional premise.
Subduction angle > 45 degrees -> Arc distance > 200 km.
To establish the relationship between tectonic plate angle and arc distance.
2
Identify and diagram the second conditional premise.
Arc distance > 200 km -> NOT (Produces tholeiitic basalt exclusively).
To establish the relationship between arc distance and basalt composition.
3
Combine the first two premises into a transitive logical chain.
Subduction angle > 45 degrees -> NOT (Produces tholeiitic basalt exclusively).
To connect the initial condition (angle) to the final outcome (basalt composition).
4
Form the contrapositive of the transitive chain.
Produces tholeiitic basalt exclusively -> NOT (Subduction angle > 45 degrees), which means Subduction angle is 45 degrees or less.
To determine what must be true when the necessary condition is reversed and negated.
5
Apply the quantifier premise to the contrapositive rule.
Since MOST Cenozoic Belt arcs produce tholeiitic basalt exclusively, MOST Cenozoic Belt arcs must have subduction angles of 45 degrees or less.
To synthesize the formal logic chain with the factual quantifier provided in the stimulus, yielding the final provable deduction.

Anahtar Kavram

Chaining Conditional Statements and Quantifier Application
Soru 153Soru →

A deep-sea research station operates under strict automated environmental control protocols. Match each set of protocol conditions (Left) with the logically valid deduction that MUST be true based on those conditions (Right).

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Öğeler

Protocol 1: Ventilation Unit A's activation is sufficient to isolate Sector B. Sector G's activation is a necessary condition for Sector D to pressurize. However, Sector G cannot activate if Sector B is isolated.
Protocol 2: Filter E is purged unless Valve Z is secured. Manifold H failing precludes Valve Z from being secured. Furthermore, Pump T activating requires that Filter E not be purged.
Protocol 3: Generator I synchronizes if, and only if, Turbine K delays. Diagnostic L verifying depends on Generator I synchronizing. Relay M going offline is a necessary consequence of Turbine K delaying.
Protocol 4: Module N is sealed when, and only when, Hatch X is unlatched. Override O being engaged is sufficient to seal Module N. Sensor P's activation guarantees that Hatch X is latched.

Eşleşmeler

Cevabı ve açıklamayı göster

Cevap

Protocol 1 matches with the deduction about Sector D and Unit A. Protocol 2 matches with the deduction about Pump T and Manifold H. Protocol 3 matches with the deduction about Relay M and Diagnostic L. Protocol 4 matches with the deduction about Sensor P and Override O.
Each correct pairing represents a flawless deductive chain formed by translating advanced conditional indicators (sufficient, necessary, unless, requires, precludes) into formal logic, finding the linkages, and tracing the contrapositive path to an unavoidable conclusion.

Adım Adım Çözüm

1
Translate Protocol 1 into formal logic and chain the conditions.
A -> B; D -> G; B -> ~G. Chaining yields D -> G -> ~B -> ~A.
This establishes that if D pressurizes, A must be inactive, confirming the match.
2
Translate Protocol 2 into formal logic and chain the conditions.
The 'unless' statement becomes ~Z -> E (or ~E -> Z). 'Precludes' means H -> ~Z. 'Requires' means T -> ~E. Chaining yields T -> ~E -> Z -> ~H.
This proves that activating T guarantees H has not failed.
3
Translate Protocol 3 into formal logic and chain the conditions.
I <-> K; L -> I; K -> M. Forward chain: L -> I -> K -> M. Contrapositive chain: ~M -> ~K -> ~I -> ~L.
This confirms that if Relay M fails to go offline (~M), Diagnostic L does not verify (~L).
4
Translate Protocol 4 into formal logic and chain the conditions.
N <-> X_unlatched; O -> N; P -> X_latched (which is ~X_unlatched). Chain: P -> ~X_unlatched -> ~N -> ~O.
This proves that Sensor P activating guarantees Override O is not engaged.

Anahtar Kavram

Chaining Conditional Statements through advanced linguistic triggers and contrapositives.
Soru 154Soru →

All architectural restoration projects funded by the Heritage Foundation require the use of traditional masonry techniques. Furthermore, any restoration project that requires traditional masonry techniques must source its raw materials from suppliers within the same county. No project that sources its raw materials from suppliers within the same county is exempt from undergoing a comprehensive regional environmental review. Recently released records indicate that at least some architectural restoration projects funded by the Heritage Foundation are completed ahead of their projected schedules.

Based on the information above, which one of the following must be true?

Cevabı ve açıklamayı göster

Cevap: At least some architectural restoration projects that are completed ahead of their projected schedules are not exempt from undergoing a comprehensive regional environmental review.

Cevap

At least some architectural restoration projects that are completed ahead of their projected schedules are not exempt from undergoing a comprehensive regional environmental review.
The correct answer properly combines the stimulus's conditional chain with its quantifier. The premises dictate that all Heritage Foundation projects must ultimately undergo the environmental review (they are not exempt). Because we are told that at least some Heritage Foundation projects are completed ahead of schedule, there is an unavoidable overlap: those specific projects that finish early must also be subject to the review.

Adım Adım Çözüm

1
Map the formal logic chain of absolute conditions provided in the stimulus.
Heritage Foundation (HF) -> Traditional Masonry (TM) -> Local Sourcing (LS) -> NOT Exempt from Review (~ER).
This establishes that every single HF project ultimately must undergo the regional environmental review (HF -> ~ER).
2
Identify and map the quantifier statement.
HF 'some' Ahead of Schedule (AS).
This tells us that the properties of HF apply to at least a portion of the projects that finish early.
3
Combine the formal logic chain with the quantifier statement to find the necessary overlap.
Since HF 'some' AS, and all HF -> ~ER, it must logically be true that AS 'some' ~ER.
If an entity possesses two characteristics simultaneously (being an HF project and finishing ahead of schedule), any mandatory rule applying to the first characteristic (not being exempt) must also overlap with the second.

Anahtar Kavram

Chaining Conditional Logic with Quantifiers
Soru 155Soru →

According to the new international guidelines for clinical pharmaceutical trials, a trial advances to Phase III only if it demonstrates long-term efficacy. Furthermore, unless a trial is monitored for secondary adverse effects, it cannot demonstrate long-term efficacy. Every trial that is monitored for secondary adverse effects must be subject to a rigorous independent ethics review. Finally, a newly developed treatment contains synthetic bio-markers only if it advances to Phase III.

Based on the guidelines above, which one of the following must be true?

Cevabı ve açıklamayı göster

Cevap: Any newly developed treatment that contains synthetic bio-markers is subject to a rigorous independent ethics review.

Cevap

Any newly developed treatment that contains synthetic bio-markers is subject to a rigorous independent ethics review.
The correct answer accurately connects the beginning of the logical chain to the end. The stimulus establishes: (1) Synthetic bio-markers require Phase III; (2) Phase III requires long-term efficacy; (3) Long-term efficacy requires monitoring for secondary effects; and (4) Monitoring requires an independent ethics review. Linking these together yields: Synthetic bio-markers → Ethics review.

Adım Adım Çözüm

1
Translate the conditional rules regarding Phase III and efficacy.
Rule 1: Advances to Phase III → Demonstrates long-term efficacy. Rule 2: 'Unless monitored, cannot demonstrate efficacy' translates to 'If it demonstrates efficacy → Monitored for secondary effects'.
Accurate translation of indicator words like 'only if' and 'unless' is required to establish the logical relationships.
2
Translate the remaining rules and combine all statements into a single transitive chain.
Rule 3: Monitored for secondary effects → Independent ethics review. Rule 4: Contains synthetic bio-markers → Advances to Phase III. Combined Chain: Contains synthetic bio-markers → Advances to Phase III → Demonstrates long-term efficacy → Monitored for secondary effects → Independent ethics review.
Creating a unified logical sequence makes it possible to see the direct relationship between the first sufficient condition and the final necessary condition.
3
Evaluate the options against the established logical chain.
The chain proves that if a treatment contains synthetic bio-markers, it must ultimately be subject to an independent ethics review.
This confirms that the correct answer is a valid deduction drawn from linking the first term to the last term.

Anahtar Kavram

Chaining Conditional Statements
Soru 156Soru →

Match each set of corporate policy premises with the logically valid deduction that can be derived by chaining them.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Öğeler

If a project undergoes an External Audit, it must receive Budget Approval. A project receives Budget Approval only if it passes the Compliance Review.
The Director will Sign-off on a project whenever it passes the Compliance Review. Unless the Executive Board Reviews it, the Director will not Sign-off on the project.
Final Implementation occurs only if the Executive Board Reviews the project. If a project undergoes an External Audit, then Final Implementation will occur.
A project is Signed-off by the Director whenever it receives Budget Approval. Unless a project undergoes an External Audit, it will not be Signed-off by the Director.

Eşleşmeler

Cevabı ve açıklamayı göster

Cevap

Set 1 pairs with the deduction about Compliance and Audit; Set 2 pairs with the deduction about Executive Board and Compliance; Set 3 pairs with the deduction about Audit and Executive Board; Set 4 pairs with the deduction about Audit and Budget.
Each premise set forms a transitive chain of conditionals (A -> B -> C), and the matching right item represents either the direct inference (A -> C) or its valid contrapositive (~C -> ~A).

Adım Adım Çözüm

1
Translate the premises of the first set into formal logic.
External Audit -> Budget Approval; Budget Approval -> Compliance Review.
Identifying the sufficient and necessary conditions allows us to form a logical chain.
2
Chain the premises of the first set and find the contrapositive.
Chain: External Audit -> Compliance Review. Contrapositive: ~Compliance Review -> ~External Audit.
This matches the right item stating 'If a project does not pass the Compliance Review, it does not undergo an External Audit.'
3
Translate the premises of the second set into formal logic.
Compliance Review -> Director Sign-off; Director Sign-off -> Executive Board Review.
'Whenever' introduces a sufficient condition. 'Unless X, not Y' translates to Y -> X.
4
Chain the premises of the second set and find the contrapositive.
Chain: Compliance Review -> Executive Board Review. Contrapositive: ~Executive Board Review -> ~Compliance Review.
This matches the right item stating 'If the Executive Board does not Review a project, then it has not passed the Compliance Review.'
5
Translate and chain the third set.
Final Implementation -> Executive Board Review; External Audit -> Final Implementation. Chain: External Audit -> Executive Board Review.
This directly matches the right item 'Any project that undergoes an External Audit must be Reviewed by the Executive Board.'
6
Translate and chain the fourth set.
Budget Approval -> Director Sign-off; Director Sign-off -> External Audit. Chain: Budget Approval -> External Audit. Contrapositive: ~External Audit -> ~Budget Approval.
This matches the right item stating 'If a project does not undergo an External Audit, it does not receive Budget Approval.'

Anahtar Kavram

Chaining Conditional Statements
Tahmini Süre:2m 0s
Soru 157Soru →

Company policy documentation states the following:

All employees who hold a Level 4 security clearance have passed a rigorous background check. No one who has passed a rigorous background check has a history of financial insolvency. Every employee assigned to the Quantum Project holds a Level 4 security clearance. Furthermore, some employees who hold a Level 4 security clearance are recent college graduates.

Based on the information above, which of the following statements must be true? Select all that apply.

Geçerli olan tümünü seçin

Cevabı ve açıklamayı göster

Cevap: No employee assigned to the Quantum Project has a history of financial insolvency.; At least some recent college graduates have passed a rigorous background check.

Cevap

The statements that must be true are: 'No employee assigned to the Quantum Project has a history of financial insolvency' and 'At least some recent college graduates have passed a rigorous background check.'
The correct statements are derived through valid logical deductions directly from the text. First, chaining the premises 'Every employee assigned to the Quantum Project holds a Level 4 security clearance', 'All employees with Level 4 clearance have passed a rigorous background check', and 'No one who has passed a rigorous background check has a history of financial insolvency' logically proves that no Quantum Project employee has a history of financial insolvency. Second, combining the premise 'some employees who hold a Level 4 clearance are recent college graduates' with 'All employees with Level 4 clearance have passed a rigorous background check' guarantees that at least some recent college graduates have passed the rigorous background check.

Adım Adım Çözüm

1
Translate the statements into formal logical notation.
1. L4 -> BC
2. BC -> ~FI
3. QP -> L4
4. L4 -some-> RCG
Mapping the premises allows for precise chaining and prevents bringing in outside assumptions.
2
Chain the conditional statements together.
QP -> L4 -> BC -> ~FI
Connecting the sufficient and necessary conditions reveals guaranteed deductions across the entire chain.
3
Evaluate the 'some' statement against the established chain.
Since L4 -some-> RCG, and L4 -> BC, we can deduce RCG -some-> BC.
If a subset (some recent college graduates) possesses a characteristic (Level 4), they must also possess all characteristics guaranteed by that characteristic (Background Check).
4
Evaluate the choices against the established valid deductions and eliminate logical fallacies.
The two correct statements match our deductions perfectly. The other three choices represent an illegal reversal, an unwarranted assumption of set overlap, and an illegal negation.
Must Be True questions require 100% provable answers. Any choice relying on a logical flaw must be eliminated.

Anahtar Kavram

Chaining conditional statements and correctly integrating quantifier logic ('some') without making unwarranted assumptions.
Soru 158Soru →

Read the following stimulus and evaluate the statement below.

Stimulus: To qualify for a municipal architectural preservation grant, a building must have been constructed prior to 1930 and must retain its original exterior facade. Furthermore, any building that retains its original exterior facade is automatically exempt from the city's modern exterior cladding regulations. The Wellington Building was constructed in 1928 and is exempt from the modern exterior cladding regulations.

Statement: Based on the information provided, it must be true that the Wellington Building qualifies for the municipal architectural preservation grant.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False
The statement is false because the conclusion relies on an illegal reversal. The stimulus establishes that retaining an original facade guarantees an exemption from modern exterior cladding regulations. However, it does not state that the ONLY way to be exempt is to retain the original facade. Since the Wellington Building might be exempt for a different reason, we cannot definitively conclude it retains its original facade, and therefore we cannot conclude it qualifies for the grant.

Adım Adım Çözüm

1
Diagram the first conditional statement regarding the grant.
Grant -> Constructed Before 1930 AND Retains Original Facade
To identify the necessary conditions for a building to qualify for the architectural preservation grant.
2
Diagram the second conditional statement regarding the exemption.
Retains Original Facade -> Exempt from Cladding Regulations
To establish the relationship between the facade and the cladding regulations.
3
Analyze the known facts about the Wellington Building.
Wellington Building = Constructed Before 1930 (1928) AND Exempt from Cladding Regulations.
To see if the known facts satisfy the necessary conditions for the grant.
4
Determine if the Wellington Building must retain its original facade.
We cannot determine this. Being exempt from cladding regulations is a necessary condition of retaining the original facade, but it is not a sufficient condition.
Concluding that the building has its original facade based on its exemption status would be an illegal reversal.
5
Evaluate the final statement.
Because we cannot prove the Wellington Building retains its original facade, we cannot prove it qualifies for the grant.
A 'Must Be True' statement requires 100% certainty based only on the provided premises.

Anahtar Kavram

Evaluating Must Be True inferences and avoiding Illegal Reversals in conditional logic.
Soru 159Soru →

If the proposed highway expansion is approved, the adjacent wetlands will be drained. The wetlands will be drained only if the local wildlife council's objections are overruled. Furthermore, any drainage of the wetlands will result in a decline in the migratory bird population, and a decline in this population always leads to a drop in eco-tourism revenue.

Which one of the following statements must be true based on the information above?

Cevabı ve açıklamayı göster

Cevap: If local eco-tourism revenue does not drop, then the proposed highway expansion was not approved.

Cevap

If local eco-tourism revenue does not drop, then the proposed highway expansion was not approved.
The stimulus establishes a direct sequence of conditional statements: Highway Approved -> Wetlands Drained -> Bird Decline -> Revenue Drop. The valid contrapositive of this entire sequence is: No Revenue Drop -> Highway Not Approved. The correct answer precisely states this logically guaranteed outcome.

Adım Adım Çözüm

1
Formalize the conditional statements presented in the stimulus.
1. Highway Approved -> Wetlands Drained
2. Wetlands Drained -> Objections Overruled
3. Wetlands Drained -> Bird Decline
4. Bird Decline -> Revenue Drop
Translating English statements into formal logical notation reveals their precise relationships.
2
Identify the primary conditional chain that connects the majority of the variables.
Highway Approved -> Wetlands Drained -> Bird Decline -> Revenue Drop
Chaining allows us to see the ultimate necessary outcomes of the initial sufficient trigger.
3
Determine the valid contrapositive of the combined conditional chain.
No Revenue Drop -> No Bird Decline -> No Wetlands Drained -> Highway Not Approved
In 'Must Be True' formal logic questions, the correct answer is frequently the contrapositive of the main logical chain.

Anahtar Kavram

Chaining Conditional Statements
Soru 160Soru →

According to the newly ratified International Trade Arbitration framework, a penalized nation will have its economic sanctions lifted only if it submits to a binding independent audit. However, a penalized nation cannot submit to a binding independent audit unless it formally waives its right to appeal the tribunal's preliminary ruling. Furthermore, any nation that formally waives its right to appeal the tribunal's preliminary ruling will automatically be stripped of its emergency tariff protections. It is a strict rule of the framework that a penalized nation retains its emergency tariff protections if it maintains its original trade embargo.

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

Cevabı ve açıklamayı göster

Cevap: Any penalized nation that maintains its original trade embargo will not have its economic sanctions lifted.

Cevap

Any penalized nation that maintains its original trade embargo will not have its economic sanctions lifted.
The correct answer accurately reflects the contrapositive chain of the stimulus. By linking the premises, we establish that if sanctions are lifted (SL), the nation must not maintain its embargo (~ME), represented as SL -> ~ME. The contrapositive of this relationship is ME -> ~SL, meaning if a nation maintains its embargo, its sanctions cannot be lifted.

Adım Adım Çözüm

1
Diagram the first sentence.
Sanctions Lifted (SL) -> Independent Audit (IA)
The phrase 'only if' introduces a necessary condition.
2
Diagram the second sentence.
Independent Audit (IA) -> Waives Appeal (WA)
The phrase 'cannot... unless' translates to '~WA -> ~IA', which contraposes to 'IA -> WA'.
3
Diagram the third sentence.
Waives Appeal (WA) -> Stripped of Protections (~RP)
The phrase 'any... will automatically' introduces a sufficient condition. Note that 'stripped of protections' is the logical negation of 'retains protections' (RP).
4
Diagram the fourth sentence.
Maintains Embargo (ME) -> Retains Protections (RP)
The phrase 'retains... if it maintains' places the condition following 'if' as the sufficient condition.
5
Create a unified conditional chain.
SL -> IA -> WA -> ~RP. The contrapositive of the fourth premise is ~RP -> ~ME. Combining them yields: SL -> IA -> WA -> ~RP -> ~ME.
Linking the common terms allows us to see the full transitive relationship.
6
Derive the full contrapositive chain to find the correct answer.
ME -> RP -> ~WA -> ~IA -> ~SL
The correct answer often relies on reading the contrapositive chain from left to right. 'ME -> ~SL' perfectly matches the correct option.

Anahtar Kavram

Chaining Conditional Statements
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