Inference and Deduction

215 soru

Soru 1Soru →

According to the municipal zoning code, any city planner who approves the designation of a High-Density Residential Zone (HDRZ) in a given neighborhood must first complete a Comprehensive Traffic Impact Study (CTIS) for that neighborhood. Completing a CTIS requires that the planner consult with both the Regional Transit Authority and the neighborhood's local association. However, formal consultation with a neighborhood's local association is impossible if that neighborhood lacks a legally registered civic charter. Currently, none of the neighborhoods located within the historic Westside district possess a legally registered civic charter.

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

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Cevap: No city planner has approved the designation of a High-Density Residential Zone in any neighborhood within the historic Westside district.

Cevap

No city planner has approved the designation of a High-Density Residential Zone in any neighborhood within the historic Westside district.
The correct answer accurately reflects the contrapositive of the stimulus's logical chain. The text establishes that approving an HDRZ requires completing a CTIS, which requires consulting the local association. It also establishes that this consultation requires a civic charter. Because no neighborhood in the Westside district has a civic charter, it is impossible to consult their local associations. Consequently, a CTIS cannot be completed, meaning a city planner cannot approve an HDRZ there.

Adım Adım Çözüm

1
Diagram the primary conditional statements provided in the municipal zoning rules.
HDRZ Approved → CTIS Completed → (Consult RTA AND Consult Local Association).
To establish the necessary prerequisites for a city planner to legally approve a high-density zone.
2
Diagram the restriction regarding neighborhood civic charters.
No Civic Charter → Local Association Cannot be Consulted.
To integrate the limiting condition into the logical framework.
3
Form the contrapositive logical chain combining all premises.
No Civic Charter → Local Association Cannot be Consulted → CTIS Cannot be Completed → HDRZ Cannot be Approved.
To determine the unavoidable consequences when a neighborhood lacks a civic charter.
4
Apply the specific factual premise about the Westside district to the contrapositive chain.
Westside Neighborhood → No Civic Charter → HDRZ Cannot be Approved.
To draw a definitive conclusion that must be true based entirely on the provided text.

Anahtar Kavram

Chaining conditional statements and applying the contrapositive to draw a guaranteed deduction.
Soru 2Soru →

Botanists studying a temperate rainforest have established that any fungal species producing the enzyme lignase can successfully break down mature hardwood. Furthermore, most fungal species inhabiting the rainforest's upper canopy produce lignase, though no upper-canopy fungal species can survive prolonged freezing temperatures. Interestingly, every fungal species capable of breaking down mature hardwood requires a highly humid microclimate to reproduce, unless that species is capable of surviving prolonged freezing temperatures.

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

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Cevap: Most fungal species inhabiting the rainforest's upper canopy require a highly humid microclimate to reproduce.

Cevap

Most fungal species inhabiting the rainforest's upper canopy require a highly humid microclimate to reproduce.
The correct answer is derived by chaining the provided facts. First, because most canopy fungi produce lignase, and all lignase producers break down hardwood, most canopy fungi break down hardwood. Second, we know absolutely no canopy fungi survive freezing. The final rule dictates that any fungus breaking down hardwood must require a humid microclimate, UNLESS it can survive freezing. Since the canopy fungi that break down hardwood cannot survive freezing, the 'unless' exception does not apply to them. Therefore, this majority group of canopy fungi must require a humid microclimate.

Adım Adım Çözüm

1
Connect the 'most' quantifier to the first conditional rule.
Since most canopy species produce lignase, and all lignase producers break down hardwood, it follows that most canopy species break down hardwood.
This establishes a core characteristic (breaking down hardwood) that applies to the majority of the canopy species.
2
Analyze the restriction on canopy species regarding temperature.
No canopy species can survive prolonged freezing temperatures.
This establishes a universal negative characteristic for the entire canopy group.
3
Translate the 'unless' clause in the final premise into a standard conditional statement.
If a species breaks down hardwood AND cannot survive freezing temperatures, then it requires a highly humid microclimate.
The word 'unless' introduces a necessary condition negated. Thus, 'Requires Humid unless Survives Freezing' means 'If NOT Survives Freezing -> Requires Humid'.
4
Apply the conditional rule from Step 3 to the group identified in Steps 1 and 2.
Since most canopy species break down hardwood AND cannot survive freezing, most canopy species must require a highly humid microclimate.
The sufficient conditions for the final premise are entirely met by the majority of the canopy group.

Anahtar Kavram

Combining formal logic conditionals, 'unless' translations, and quantifier chaining.
Soru 3Soru →

According to city records, every commercial project approved by the Planning Board this year required an environmental impact study. Furthermore, any project that requires an environmental impact study is subject to a 60-day public review period. Records also indicate that most of the commercial projects approved by the Planning Board this year received a municipal development grant. However, under city charter, no project that receives a municipal development grant is exempt from the city's prevailing wage ordinance.

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

Geçerli olan tümünü seçin

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Cevap: Every commercial project approved by the Planning Board this year is subject to a 60-day public review period.; At least some projects subject to a 60-day public review period are not exempt from the city's prevailing wage ordinance.

Cevap

The correct answers are the statement that every commercial project approved this year is subject to the review period, and the statement that at least some projects subject to the review period are not exempt from the wage ordinance.
Both correct statements can be logically deduced with complete certainty. The first follows directly from chaining two absolute rules: if a project is an approved commercial project, it needs an environmental study, and if it needs an environmental study, it requires a public review period. The second follows by combining quantifiers: since all approved commercial projects undergo public review, and most of them receive a grant (which means they cannot be exempt from the wage ordinance), it must be true that at least some projects undergoing public review are not exempt from the wage ordinance.

Adım Adım Çözüm

1
Diagram the absolute conditional statements to form a logical chain.
Commercial Project (CP) → Environmental Impact Study (EIS) → Public Review Period (PRP).
To establish the guaranteed baseline properties of all commercial projects approved this year.
2
Diagram the quantifier statements and negative conditional rules.
CP -[most]→ Municipal Grant (MG), and MG → Not Exempt (~Exempt).
To identify what is true for the majority of these commercial projects.
3
Synthesize the chains to find derivative inferences.
Since all CP are PRP, and most CP are MG (which means most CP are ~Exempt), there is an overlap: some things that are PRP must also be ~Exempt.
To systematically pre-phrase the necessary truths before evaluating the choices.

Anahtar Kavram

Drawing formal logic deductions by combining transitive conditional chains with proportion quantifiers (some/most).
Tahmini Süre:1m 45s
Soru 4Soru →

In an effort to promote sustainable industrial practices, the regional council has updated its environmental protection statutes. Under the new guidelines, a manufacturing facility is exempt from the annual carbon surcharge only if it relies primarily on renewable energy sources and does not discharge unmonitored effluent into adjacent waterways.

Which statement is logically equivalent to the principle governing the carbon surcharge exemption?

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Cevap: If a manufacturing facility either does not rely primarily on renewable energy sources or discharges unmonitored effluent into adjacent waterways, then it is not exempt from the annual carbon surcharge.

Cevap

The statement asserting that if a manufacturing facility either does not rely primarily on renewable energy sources or discharges unmonitored effluent into adjacent waterways, then it is not exempt from the annual carbon surcharge.
The correct answer accurately forms the contrapositive of the principle in the stimulus. The stimulus establishes a conditional relationship where being exempt from the surcharge requires two necessary conditions: relying on renewable energy AND not discharging unmonitored effluent. To form the logically valid contrapositive, we must reverse the conditions and negate them. Negating a compound condition joined by 'and' requires applying De Morgan's laws, changing the 'and' to 'or' while negating both individual terms. Thus, the condition becomes 'does not rely on renewable energy OR discharges unmonitored effluent'. Placing this in the sufficient condition yields a statement that perfectly matches the correct option.

Adım Adım Çözüm

1
Analyze the logical structure of the stimulus to identify the sufficient and necessary conditions.
Sufficient condition: Exempt from surcharge. Necessary condition: (Relies on renewable energy AND Does not discharge unmonitored effluent).
The phrase 'only if' introduces a necessary condition. Accurate baseline translation is required before manipulating the logic.
2
Begin forming the contrapositive by reversing the positions of the conditions and negating both sides.
NOT (Relies on renewable energy AND Does not discharge unmonitored effluent) -> NOT Exempt from surcharge.
A conditional statement is always logically equivalent to its contrapositive, which requires both reversal and negation.
3
Apply De Morgan's laws to simplify the negated compound necessary condition.
The negated condition becomes: '(Does NOT rely on renewable energy OR DOES discharge unmonitored effluent)'.
De Morgan's laws state that the negation of an 'AND' statement becomes an 'OR' statement where both individual terms are negated.
4
Combine the simplified terms to state the final, logically equivalent conditional statement.
If a facility does NOT rely on renewable energy OR it DOES discharge unmonitored effluent -> it is NOT exempt from the surcharge.
This completes the formation of the logically valid contrapositive, leading directly to the correct answer choice.

Anahtar Kavram

Forming Contrapositives of Compound Conditionals using De Morgan's Laws
Soru 5Soru →

Under the revised maritime regulations, all commercial freight vessels operating within the Obsidian Strait are required to feature double-layered hulls. Furthermore, any vessel featuring a double-layered hull incurs a maintenance cost that is significantly higher than that of a standard single-hulled ship. According to recent shipping logs, most of the vessels currently operating within the Obsidian Strait are commercial freight vessels.

If all of the statements above are true, which one of the following can be logically inferred?

Cevabı ve açıklamayı göster

Cevap: Most of the vessels currently operating within the Obsidian Strait incur a maintenance cost that is significantly higher than that of a standard single-hulled ship.

Cevap

Most of the vessels currently operating within the Obsidian Strait incur a maintenance cost that is significantly higher than that of a standard single-hulled ship.
The stimulus establishes a formal logic chain: all commercial freight vessels in the Obsidian Strait must have double-layered hulls, and all vessels with double-layered hulls incur higher maintenance costs. By combining these premises, we can deduce that all commercial freight vessels in the Obsidian Strait incur higher maintenance costs. Furthermore, the text establishes that most of the vessels currently operating in the Strait are commercial freight vessels. If most of the vessels in the Strait belong to a category that universally incurs higher maintenance costs, it must logically follow that most vessels in the Strait incur higher maintenance costs.

Adım Adım Çözüm

1
Analyze the conditional statements provided in the stimulus.
Premise 1: If a commercial freight vessel operates in the Obsidian Strait, it has a double-layered hull. Premise 2: If a vessel has a double-layered hull, it has higher maintenance costs.
To establish the formal logical rules governing the scenario.
2
Combine the conditional premises into a logical chain.
If a commercial freight vessel operates in the Obsidian Strait, it incurs higher maintenance costs.
Transitive property of formal logic (A implies B, and B implies C; therefore A implies C).
3
Apply the quantifier statement to the logical chain to determine the necessary inference.
Since 'most' vessels operating in the Strait are commercial freight vessels, and 'all' of those incur higher maintenance costs, it follows that 'most' vessels in the Strait must incur higher maintenance costs.
To deduce a final truth by applying a universal rule to a majority subgroup.

Anahtar Kavram

Combining formal conditional logic chains with quantifier statements ('most') to draw a valid necessary inference.
Tahmini Süre:1m 30s
Soru 6Soru →

In order to qualify for the accelerated development grant, a local infrastructure project must be classified as high-priority by the regional council and must secure matching private investments. Any infrastructure project that secures matching private investments is subject to the strict environmental oversight of the federal preservation board. However, no project proposed by the municipal transit authority is subject to this strict environmental oversight. Nevertheless, some projects proposed by the municipal transit authority are classified as high-priority by the regional council.

If the statements above are true, which one of the following cannot be true?

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Cevap: A project proposed by the municipal transit authority qualifies for the accelerated development grant.

Cevap

The option stating that a project proposed by the municipal transit authority qualifies for the accelerated development grant cannot be true.
The stimulus establishes a conditional chain that rules out municipal transit authority projects from qualifying for the grant. To qualify for the accelerated development grant, a project must secure matching private investments. Any project with matching private investments is subject to strict environmental oversight. Therefore, qualifying for the grant strictly requires being subject to environmental oversight. However, the stimulus explicitly states that no project proposed by the municipal transit authority is subject to this oversight. Consequently, no municipal transit authority project can ever secure matching private investments, making it impossible for any such project to satisfy the necessary conditions for the grant.

Adım Adım Çözüm

1
Map the conditions required to qualify for the grant.
Grant -> High-Priority AND Matching Investments.
Translating the text into formal logic simplifies the complex conditional rules.
2
Map the consequences of securing matching investments.
Matching Investments -> Strict Oversight.
Connecting terms allows us to build a deductive chain.
3
Map the rules regarding the municipal transit authority.
Transit Authority -> NOT Strict Oversight. (Additionally, Transit Authority -some- High-Priority).
Identifying absolute constraints on specific entities reveals logical impossibilities.
4
Combine the rules to test if a transit authority project can logically qualify for the grant.
Transit Authority -> NOT Strict Oversight -> NOT Matching Investments -> NOT Grant.
Since transit projects cannot secure matching investments, they fail a necessary condition for the grant, making their qualification logically impossible.

Anahtar Kavram

Chaining conditional statements to identify a logically impossible outcome.
Tahmini Süre:2m 0s
Soru 7Soru →

According to the newly ratified Outer Space Mining Treaty, securing a commercial extraction license on the lunar surface requires that a corporation either establish an autonomous life-support habitat or formally partner with a state-sponsored space agency.

Which one of the following statements logically follows from the treaty's requirement?

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Cevap: If a corporation neither establishes an autonomous life-support habitat nor formally partners with a state-sponsored space agency, it will not secure a commercial extraction license on the lunar surface.

Cevap

The statement that logically follows is: 'If a corporation neither establishes an autonomous life-support habitat nor formally partners with a state-sponsored space agency, it will not secure a commercial extraction license on the lunar surface.'
The correct answer accurately applies formal logic and De Morgan's laws to create a valid contrapositive. The original premise dictates: License → (Habitat OR Partner). The contrapositive requires reversing the direction and negating both sides. Crucially, negating an 'OR' statement transforms it into an 'AND' statement. Therefore, the valid inference is: If NOT Habitat AND NOT Partner (phrased as 'neither... nor'), then NOT License.

Adım Adım Çözüm

1
Identify the logical structure of the original rule in the stimulus.
Sufficient condition: Securing a commercial extraction license. Necessary condition: Establishing a habitat OR partnering with a space agency.
Mapping the exact formal logic relationship is required before evaluating conditional deductions.
2
Formulate the logical contrapositive of the rule.
To find the contrapositive, reverse the terms and negate both sides. Negating the 'OR' statement requires De Morgan's laws: 'NOT (Habitat OR Partner)' becomes 'NOT Habitat AND NOT Partner'.
The only statement that definitively must be true based on a conditional premise is its logically valid contrapositive.
3
Match the formulated contrapositive to the answer choices.
The correct deduction is: If a corporation does NOT establish a habitat AND does NOT partner with an agency (neither... nor), then it CANNOT secure a license.
This eliminates choices that contain formal logical fallacies such as mistaken reversals, mistaken negations, or incomplete applications of De Morgan's laws.

Anahtar Kavram

Forming valid contrapositives from compound conditional statements using De Morgan's laws.
Soru 8Soru →

According to the university's revised grant allocation rules, a research proposal is designated as a 'Priority-1' initiative only if it demonstrates formal interdisciplinary collaboration. Formal interdisciplinary collaboration is achieved if, and only if, the project team includes researchers from at least three distinct faculties. Furthermore, any project team that includes researchers from at least three distinct faculties requires a dedicated administrative manager, unless the proposal's principal investigator holds a tenured professorship. Finally, no proposal can be designated as a 'Priority-1' initiative if it relies on external corporate funding.

Which one of the following conclusions can be properly drawn from the university's revised grant allocation rules?

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Cevap: If a proposal whose principal investigator does not hold a tenured professorship is designated as a 'Priority-1' initiative, then the project team requires a dedicated administrative manager and the proposal cannot rely on external corporate funding.

Cevap

The conclusion stating that a 'Priority-1' proposal without a tenured principal investigator must require a dedicated administrative manager and cannot rely on external corporate funding is the correct deduction.
The correct answer seamlessly synthesizes all four rules into a single valid deduction. The stimulus establishes that a 'Priority-1' designation triggers a chain of requirements: it absolutely requires 'interdisciplinary collaboration', which means it strictly requires 'three distinct faculties'. Having 'three distinct faculties' requires at least one of two things: a 'dedicated administrative manager' or a 'tenured principal investigator'. If the proposal lacks a 'tenured principal investigator', it is mathematically forced to satisfy the other half of the requirement, thus needing a 'dedicated administrative manager'. Concurrently, the final rule guarantees that a 'Priority-1' designation completely precludes 'external corporate funding'.

Adım Adım Çözüm

1
Translate the conditional statements into symbolic logic.
1) Priority-1 (P1) -> Interdisciplinary Collaboration (IC). 2) IC <-> Three Faculties (3F). 3) 3F -> (Dedicated Manager (DM) OR Tenured PI (TP)). 4) Corporate Funding (CF) -> ~P1 (Contrapositive: P1 -> ~CF).
Formalizing the text prevents the misinterpretation of complex indicator words like 'only if', 'if and only if', and 'unless'.
2
Chain the conditional statements together where the necessary condition of one matches the sufficient condition of another.
P1 -> IC <-> 3F -> (DM OR TP). Additionally, P1 -> ~CF.
Creating a deductive chain reveals the absolute downstream requirements triggered by any given sufficient condition.
3
Evaluate the correct answer by applying its specific sufficient conditions (P1 and ~TP) to the established chain.
If P1 is true, then 3F must be true, which subsequently requires either DM or TP to be true. Since ~TP is given by the answer choice, DM must logically be true. Also, since P1 is true, ~CF must be true. Therefore, P1 + ~TP strictly guarantees DM + ~CF.
This confirms that the correct answer is an unbroken, valid deduction directly supported by combining all the premises.

Anahtar Kavram

Diagramming and synthesizing complex conditional chains involving compound sufficient/necessary conditions and 'unless' indicators.
Soru 9Soru →

When a city installs automated red-light cameras at an intersection, the number of right-angle collisions typically decreases significantly, as fewer drivers attempt to run the red light. However, at intersections where these cameras are installed, the total number of collisions often remains unchanged or even increases. This is because the decrease in right-angle collisions is usually offset by a substantial increase in rear-end collisions, which happen when drivers brake abruptly to avoid being ticketed. Traffic safety data indicates that rear-end collisions are, on average, much less likely to result in severe injuries than right-angle collisions are.

Which one of the following is most strongly supported by the information above?

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Cevap: The installation of automated red-light cameras at an intersection tends to reduce the overall number of severe injuries resulting from collisions at that intersection.

Cevap

The installation of automated red-light cameras at an intersection tends to reduce the overall number of severe injuries resulting from collisions at that intersection.
The text demonstrates a shift in the composition of accidents at intersections with red-light cameras. While the total number of accidents stays the same or goes up slightly, the proportion shifts away from right-angle collisions toward rear-end collisions. Because the text explicitly states that rear-end collisions are 'much less likely to result in severe injuries', substituting a more dangerous accident type for a less dangerous one—even if the total number of accidents remains constant—strongly supports the inference that the overall number of severe injuries will decrease at these locations.

Adım Adım Çözüm

1
Analyze the causal relationships presented in the stimulus.
Installing cameras causes right-angle collisions to decrease and rear-end collisions to increase.
Understanding the direct effects of the cameras is necessary to evaluate the outcomes.
2
Evaluate the net effect on the total volume of collisions.
The total number of collisions remains unchanged or increases slightly because the rise in rear-end collisions offsets the drop in right-angle collisions.
This establishes that the overall frequency of accidents does not drastically drop, meaning any reduction in injuries must come from the change in accident *type*.
3
Combine the frequency data with the severity data provided at the end of the stimulus.
The intersection is experiencing roughly the same number of total accidents, but a large portion of highly dangerous accidents (right-angle) has been replaced by less dangerous accidents (rear-end).
Synthesizing frequency with severity allows us to draw a strongly supported conclusion about the overall injury rate.
4
Formulate the most strongly supported inference.
Because the new mix of accidents is less prone to causing severe injuries, the overall number of severe injuries at that intersection likely goes down.
This directly matches the correct answer choice.

Anahtar Kavram

Synthesizing shifting proportions (accident types) with differing rates (injury likelihood) to infer a net outcome.
Soru 10Soru →

Under the new environmental directives, any regional municipality that enacts a comprehensive water conservation protocol must either increase its baseline utility rates or secure a federal sustainability grant. A municipality is eligible to secure a federal sustainability grant only if it demonstrates a verifiable reduction in agricultural runoff. However, municipalities situated in the historically drought-prone Arid Basin region are strictly prohibited by state mandate from increasing their baseline utility rates. The municipality of Oakhaven, which is situated in the Arid Basin region, has recently enacted a comprehensive water conservation protocol.

Which of the following must be true on the basis of the statements above?

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Cevap: Oakhaven has demonstrated a verifiable reduction in agricultural runoff.

Cevap

The correct inference is that Oakhaven has demonstrated a verifiable reduction in agricultural runoff.
The correct answer accurately synthesizes the conditional statements provided in the stimulus. Because Oakhaven enacted the protocol, it is required to either increase its utility rates or secure a grant. Since state law prohibits Arid Basin municipalities from increasing rates, Oakhaven is left with only one option: securing the grant. Securing the grant inherently requires a verifiable reduction in agricultural runoff, meaning Oakhaven must have met this requirement.

Adım Adım Çözüm

1
Map the first conditional rule.
Enact protocol → Increase rates OR Secure grant.
To establish the required consequences for any municipality enacting the protocol.
2
Map the second conditional rule regarding grants.
Secure grant → Demonstrate reduction in runoff.
To identify the necessary condition for receiving a federal grant.
3
Apply the geographic constraint to Oakhaven.
Oakhaven is in the Arid Basin, so it cannot increase its baseline utility rates.
To eliminate one of the two possible outcomes of enacting the protocol.
4
Chain the logic together for Oakhaven.
Oakhaven enacted the protocol, but cannot increase rates. Therefore, it must secure a grant. To secure a grant, it must demonstrate a reduction in runoff.
To derive the final valid inference that must be true.

Anahtar Kavram

Chaining Conditional Statements and Eliminating Alternatives
Soru 11Soru →

Fluids emitted by deep-sea thermal vents are rich in hydrogen sulfide, a compound highly toxic to most marine organisms. Nevertheless, the shrimp species Rimicaris exoculata thrives in these environments. R. exoculata lacks a functional digestive tract; instead, it possesses enlarged gills that harbor massive colonies of a specific chemoautotrophic bacteria. These bacteria survive by oxidizing the vent's hydrogen sulfide to synthesize organic carbon compounds. Recent isotopic analysis of R. exoculata tissues demonstrates that virtually all of the carbon in the shrimp's body matches the unique isotopic signature of the carbon compounds synthesized by these gill-dwelling bacteria.

Which one of the following is most strongly supported by the information above?

Cevabı ve açıklamayı göster

Cevap: R. exoculata does not acquire a biologically significant proportion of its carbon through the ingestion of other organisms.

Cevap

R. exoculata does not acquire a biologically significant proportion of its carbon through the ingestion of other organisms.
The stimulus explicitly states two critical facts: the shrimp lacks a functional digestive tract, and 'virtually all' of the carbon in its body is synthesized by the bacteria living in its gills. If virtually all of its carbon comes directly from the bacteria, it logically follows that only an insignificant fraction (if any) could possibly come from the ingestion of other organisms. This is a very safe, direct synthesis of the provided premises.

Adım Adım Çözüm

1
Analyze the premises provided in the stimulus.
Premise 1: The shrimp lacks a functional digestive tract. Premise 2: Virtually all of the carbon in the shrimp's body comes from the specific bacteria in its gills.
Most Strongly Supported questions require synthesizing the explicit facts given without bringing in outside assumptions.
2
Synthesize the facts to formulate a safe inference.
If nearly 100% of the shrimp's carbon comes from the symbiotic bacteria, and it cannot properly digest normal food anyway, then it must not be getting its carbon by eating other organisms.
A valid inference must be highly probable given the exact wording of the premises.
3
Evaluate the options against the synthesized inference.
The correct answer accurately reflects this synthesis, while the distractors make unwarranted absolute claims or introduce information not found in the text.
Eliminating options that overreach or rely on outside information is the standard method for solving Inference questions.

Anahtar Kavram

Synthesizing explicit premises to find a safely supported deduction while avoiding extreme claims and outside information.
Soru 12Soru →

Historians analyzing the recently discovered Qumran Archive have established several facts about its manuscripts. Every manuscript in the archive that was written on vellum was authored by a member of the elite scribal class. Furthermore, most of the manuscripts in the archive that were authored by the elite scribal class contain political commentary. However, none of the manuscripts written on papyrus contain any political commentary. All of the manuscripts in the archive were written on either vellum or papyrus.

Which one of the following is most strongly supported by the information above?

Cevabı ve açıklamayı göster

Cevap: Most of the manuscripts in the archive that were authored by the elite scribal class were written on vellum.

Cevap

Most of the manuscripts in the archive that were authored by the elite scribal class were written on vellum.
Since all manuscripts in the archive are either vellum or papyrus, and none of the papyrus manuscripts contain political commentary, it must be logically true that ALL manuscripts containing political commentary are written on vellum. The stimulus explicitly states that MOST of the manuscripts authored by the elite scribal class contain political commentary. Since all of these political commentary manuscripts are on vellum, it mathematically follows that most of the manuscripts authored by the elite scribal class were written on vellum.

Adım Adım Çözüm

1
Establish the binary constraint for the manuscript materials.
Every manuscript is either vellum (V) or papyrus (P).
This structural rule dictates that any manuscript that is not papyrus must inherently be vellum.
2
Translate the conditional rules regarding political commentary.
If Papyrus -> No Political Commentary (~PC). By contrapositive, if Political Commentary (PC) -> Not Papyrus. Given Step 1, this means PC -> Vellum.
This establishes a critical bridge: every single manuscript in the archive containing political commentary is written on vellum.
3
Synthesize the quantifier rule with the derived conditional rule.
Most of the elite scribal class manuscripts contain political commentary. Since all political commentary manuscripts are vellum, these 'most' must also be vellum.
When a subset (more than half) possesses a trait, and that trait guarantees membership in a specific category (vellum), then more than half of the original overarching group must belong to that category.

Anahtar Kavram

Logical Synthesis of Quantifiers (Most/Some) with Conditional Contrapositives

Alternatif Yöntem

You can visualize this mathematically. Let E be the total number of elite scribal manuscripts. We know manuscripts with political commentary in this group (E_PC) make up more than 50% of E. Since papyrus manuscripts have no political commentary, all E_PC manuscripts must be vellum. Therefore, the number of vellum elite manuscripts is at least equal to E_PC, which means it is also greater than 50% of E.
Tahmini Süre:2m 30s
Soru 13Soru →

Consider the following premises regarding the state judiciary:

Every judge appointed to the appellate court has over a decade of trial experience. Most judges appointed to the appellate court have published legal scholarship. None of the judges who have published legal scholarship sit on the disciplinary board.

Based on these premises, the following deduction must logically be true:
Most judges with over a decade of trial experience do not sit on the disciplinary board.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

The statement is False because it commits a quantifier overreach error, attempting to apply a characteristic of a specific subset (appellate judges) to the majority of a broader superset (judges with trial experience).
The deduction provided in the stem is invalid. It correctly chains the premises to realize that most appellate judges do not sit on the board. However, it illegally extends that conclusion to state that most judges with a decade of trial experience do not sit on the board. We only know that *some* (at least the appellate judges) do not. We do not have information about the rest of the judges with trial experience.

Adım Adım Çözüm

1
Map the formal logic of the premises.
Premise 1: All Appellate Judges (AJ) -> Trial Experience (TE). Premise 2: Most AJ -> Published (P). Premise 3: No P -> Disciplinary Board (DB), which means All P -> ~DB.
Translating statements into formal notation clarifies the boundaries of the quantifier relationships.
2
Chain the 'Most' and 'None/All' premises to form a valid intermediate deduction.
Combine Premise 2 (Most AJ -> P) with Premise 3 (All P -> ~DB) to deduce: Most AJ -> ~DB (Most appellate judges do not sit on the disciplinary board).
In quantifier logic, combining a 'Most' statement with an 'All/None' statement yields a valid 'Most' statement if the 'Most' group points to the sufficient condition of the 'All' group.
3
Evaluate the relationship between the intermediate deduction and the target group.
We know 'Most AJ -> ~DB' and 'All AJ -> TE'. The deduction asks if 'Most TE -> ~DB' must be true.
We must test if the target conclusion strictly follows from the relationship between AJ and TE.
4
Determine the validity of the final deduction.
Invalid. Because AJ is a subset of TE, we can only conclude that 'Some TE -> ~DB'. We cannot conclude 'Most TE' share any characteristic because the broader group of TE judges could be infinitely larger than the AJ subset.
Moving from a subset to a superset only guarantees a 'Some' relationship, never a 'Most' relationship without additional numerical data.

Anahtar Kavram

Quantifier Logic (Some, Most, All)
Soru 14Soru →

When traditional hierarchical corporations transition to a "flat" organizational structure, they typically experience a short-term decrease in overall productivity. However, companies that implement comprehensive peer-review systems alongside the flat structure see their productivity return to pre-transition levels within six months. Companies that transition to a flat structure without implementing peer-review systems consistently report productivity levels below their pre-transition baseline even after two years. A recent industry report found that the majority of companies transitioning to a flat structure do not implement comprehensive peer-review systems. Which of the following statements are most strongly supported by the information above? (Select all that apply.)

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Cevap: Most companies that transition to a flat organizational structure will have productivity levels below their pre-transition baseline two years after the transition.; A flat organizational structure is not sufficient on its own to ensure a company maintains its pre-transition productivity levels in the long term.

Cevap

The correct statements are that most companies transitioning to a flat structure will remain below baseline productivity after two years, and that a flat structure alone is insufficient to maintain long-term productivity.
The correct choices are directly provable by combining the provided premises. Since the majority of transitioning companies do not use peer-review systems, and companies without these systems remain below baseline productivity after two years, it is strongly supported that most transitioning companies will be below baseline after two years. Furthermore, because a flat structure without a peer-review system results in long-term productivity deficits, the flat structure alone is demonstrably insufficient to maintain baseline productivity.

Adım Adım Çözüm

1
Analyze the premises provided in the stimulus.
Premise 1: Flat transition causes a short-term productivity drop. Premise 2: Flat transition + peer review leads to baseline recovery within 6 months. Premise 3: Flat transition + NO peer review leads to sub-baseline productivity even after 2 years. Premise 4: The majority of flat transitions occur without peer review.
Breaking down the stimulus into discrete logical facts is necessary to identify how they interact.
2
Synthesize the premises regarding the majority of companies.
Since the majority do not implement peer reviews (Premise 4), and those without peer reviews stay below baseline after two years (Premise 3), it logically follows that the majority of transitioning companies stay below baseline after two years.
To determine what can be most strongly inferred about the largest group mentioned in the text.
3
Evaluate the sufficiency of the organizational change.
Because implementing a flat structure without peer review leads to long-term productivity loss (Premise 3), the flat structure by itself is not enough to maintain prior productivity.
To test inferences regarding the inherent effectiveness of the flat structure alone.
4
Evaluate the incorrect options against the established facts.
The remaining options incorrectly assume conditional reversals, exaggerate the scope of the premises (applying them to 'any' company), or invent unsupported causal explanations.
To eliminate choices that fall into common logical traps on inference questions.

Anahtar Kavram

Synthesizing multiple premises to derive strongly supported inferences while avoiding extreme claims, conditional fallacies, and outside information.
Soru 15Soru →

Under the revised corporate governance code, a board of directors can legally dismiss a chief executive officer only if the board achieves a supermajority vote. Furthermore, a supermajority vote is possible only when at least one independent director concurs with the board's executive directors. According to a recent audit, most companies in the Capstone Investment portfolio have boards consisting entirely of executive directors. However, any company in the Capstone Investment portfolio that has restated its quarterly earnings this year has legally dismissed its chief executive officer.

Which of the following logically follows from the information above?

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Cevap: Most companies in the Capstone Investment portfolio have not restated their quarterly earnings this year.

Cevap

Most companies in the Capstone Investment portfolio have not restated their quarterly earnings this year.
The correct answer accurately combines the stimulus's formal logic chain with its central quantifier. The text establishes that restating earnings requires dismissing a CEO, and dismissing a CEO requires an independent director on the board. Therefore, any company that restates earnings must have an independent director (Restating Earnings -> Independent Director). Because we are told that 'most' Capstone Investment companies lack independent directors (their boards are 'entirely' executive), we can securely apply the contrapositive: most of these companies lack a necessary condition for restating earnings, and therefore, most have not restated their earnings.

Adım Adım Çözüm

1
Map the conditional relationships provided in the first two sentences.
Dismissing a CEO requires a supermajority (Dismiss CEO -> Supermajority). A supermajority requires an independent director (Supermajority -> Independent Director).
Establishing the formal logic chain allows us to identify necessary conditions. Transitivity means: Dismiss CEO -> Independent Director.
2
Map the conditional relationship in the final sentence.
Restating earnings requires dismissing the CEO (Restate Earnings -> Dismiss CEO).
Connecting this to our previous chain gives us the full logical sequence: Restate Earnings -> Dismiss CEO -> Independent Director.
3
Apply the quantifier provided in the third sentence to the full conditional chain.
Most Capstone companies have boards entirely consisting of executive directors, meaning they lack an independent director. By contrapositive (~Independent Director -> ~Dismiss CEO -> ~Restate Earnings), most Capstone companies cannot have restated their earnings.
If a necessary condition (Independent Director) is missing for the majority of a group, then the sufficient conditions (Dismissing CEO, Restating Earnings) must also be absent for the majority of that group.

Anahtar Kavram

Chaining Conditional Statements with Quantifiers
Soru 16Soru →

Under the revised 2026 Bioethics Commission guidelines, a cognitive enhancement implant can be approved for general public distribution only if the device has been demonstrated to have zero risk of inducing memory degradation, and it either significantly improves executive function or radically accelerates neural plasticity.

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

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Cevap: If a cognitive enhancement implant carries any risk of inducing memory degradation, or if it neither significantly improves executive function nor radically accelerates neural plasticity, it cannot be approved for general public distribution.

Cevap

The correct answer states that if an implant carries any risk of inducing memory degradation, or if it neither improves executive function nor accelerates neural plasticity, it cannot be approved.
The stimulus establishes a complex conditional relationship: Approval -> Zero Risk AND (Executive Function OR Neural Plasticity). To find what logically follows, we must find the contrapositive. According to formal logic and De Morgan's laws, we reverse the terms and negate them, flipping 'AND' to 'OR' and 'OR' to 'AND'. The negation of 'Zero Risk' is 'any risk'. The negation of the 'AND' is an 'OR'. The negation of '(Executive Function OR Neural Plasticity)' is 'neither Executive Function nor Neural Plasticity'. Putting this together creates the correct sufficient condition: 'any risk OR (neither Executive Function nor Neural Plasticity)'. This triggers the negated outcome: 'cannot be approved'. The correct option perfectly mirrors this structure.

Adım Adım Çözüm

1
Identify the sufficient and necessary conditions in the stimulus.
Sufficient (A): Approved for distribution. Necessary: Zero risk of memory degradation (Z) AND [Improves executive function (E) OR Accelerates neural plasticity (N)].
The phrase 'only if' introduces necessary conditions. Everything preceding 'only if' is the sufficient condition.
2
Symbolize the formal logic relationship.
A -> Z AND (E OR N).
Abstracting the text into logic symbols helps isolate the structure needed to form the contrapositive.
3
Form the contrapositive by negating both sides and reversing the arrow.
NOT [Z AND (E OR N)] -> NOT A.
The contrapositive is the only definitively true deduction that can be made from a universal conditional statement.
4
Apply De Morgan's laws to simplify the negated compound necessary condition.
The negation of 'Z AND (E OR N)' becomes 'NOT Z OR NOT (E OR N)'. Further applying De Morgan's to the inner condition yields 'NOT Z OR (NOT E AND NOT N)'.
De Morgan's laws dictate that when negating a compound statement, 'AND' changes to 'OR', and 'OR' changes to 'AND'.
5
Translate the simplified logical contrapositive back into English.
If an implant does not have zero risk (has ANY risk), OR if it lacks both benefits (NEITHER significantly improves E NOR radically accelerates N), then it cannot be approved (NOT A).
This translation matches the correct answer choice perfectly.

Anahtar Kavram

Forming complex contrapositives using De Morgan's laws
Soru 17Soru →

Match each excerpt from the newly proposed clinical bioethics regulatory framework (left) with its logically equivalent contrapositive statement (right).

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Öğeler

A therapy qualifies for expedited bioethics review only if it targets a terminal condition and has no viable alternatives.
Unless an applicant demonstrates both a compelling medical need and an absence of financial coercion, their participation in the clinical trial will be denied.
Implementation of the neural biofeedback mechanism requires that the software either undergoes independent auditing or is developed internally by the core research team.
Publishing the trial data prematurely is sufficient to both invalidate the patent application and permanently disqualify the researchers from future grants.

Eşleşmeler

Cevabı ve açıklamayı göster

Cevap

The correct mapping identifies the formal contrapositive of each conditional statement, properly applying De Morgan's Laws to compound conditions and accurately translating complex conditional indicators such as 'unless', 'requires', and 'only if'.
Each correctly paired item accurately translates the formal logic of the original natural language statement, identifies the sufficient and necessary conditions, reverses their order, and negates both sides. Where compound statements are involved, De Morgan's Laws are applied flawlessly to swap conjunctions ('and') with disjunctions ('or').

Adım Adım Çözüm

1
Analyze the 'only if' statement regarding expedited bioethics review.
Matches with the statement concluding that the therapy is ineligible.
'Only if' introduces necessary conditions (Terminal AND No Alternatives). Negating and reversing via De Morgan's Law results in 'Not Terminal OR Has Alternatives -> Ineligible'.
2
Analyze the 'unless' statement regarding clinical trial participation.
Matches with the statement beginning 'Any applicant whose participation... is permitted'.
'Unless X, Y' means 'If Not X, Y'. Here, 'If Not (Need AND Absence of Coercion) -> Denied'. The contrapositive is 'If Not Denied (Permitted) -> Need AND Absence of Coercion'.
3
Analyze the 'requires' statement regarding the biofeedback mechanism.
Matches with the statement beginning 'Whenever the software lacks independent auditing and has not been developed internally'.
'Requires' introduces a necessary compound condition (Auditing OR Internal). Reversing and negating flips OR to AND: 'NOT Auditing AND NOT Internal -> NOT Implemented'.
4
Analyze the 'sufficient' statement regarding premature publication.
Matches with the statement beginning 'If the researchers are not permanently disqualified... or the patent... is not invalidated'.
'Sufficient' introduces the sufficient condition. Premature -> (Invalidate AND Disqualify). Reversing and negating flips AND to OR: '(NOT Disqualify OR NOT Invalidate) -> NOT Premature'.

Anahtar Kavram

Forming contrapositives of compound conditional statements using De Morgan's Laws.
Soru 18Soru →

A corporation cannot be listed on the Apex Exchange unless it has undergone a comprehensive environmental audit. Only corporations that employ a dedicated sustainability officer can undergo a comprehensive environmental audit. No corporation that primarily manufactures synthetic plastics employs a dedicated sustainability officer. Furthermore, any corporation that qualifies for a municipal tax abatement either primarily manufactures synthetic plastics or fails to generate over ten million dollars in annual revenue.

Based on the information provided, any corporation listed on the Apex Exchange that qualifies for a municipal tax abatement fails to generate over ten million dollars in annual revenue.

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Cevap: True

Cevap

The statement is logically valid and therefore True.
The correct answer is True. By diagramming the premises, we derive the chain: Listed → Audit → Officer → Not Plastics. Therefore, any listed corporation cannot manufacture synthetic plastics. The stimulus also establishes: Abatement → Plastics OR Not Over 10M Revenue. If a corporation is both listed AND receives the abatement, it is automatically disqualified from the 'Plastics' option due to being listed. Therefore, by disjunctive syllogism, it must fulfill the only remaining option: failing to generate over ten million dollars in annual revenue. The statement is an undeniably valid deduction.

Adım Adım Çözüm

1
Translate the first three premises into conditional logic chains.
Listed → Audit; Audit → Officer; Plastics → ~Officer.
Identifying the formal logic relationships is required to find connections between the terms.
2
Connect the individual conditions into a single transitive chain.
Listed → Audit → Officer → ~Plastics.
Combining the rules reveals the ultimate constraint placed on any corporation listed on the Apex Exchange.
3
Diagram the disjunctive premise concerning the tax abatement.
Abatement → (Plastics OR ~Over 10M Revenue).
The 'either...or' language establishes a necessary condition containing two distinct possibilities.
4
Apply the derived rules to the specific group mentioned in the statement: corporations that are both listed and receive the abatement.
Because they are listed, they must be ~Plastics. Because they receive the abatement, they must be (Plastics OR ~Over 10M Revenue).
To evaluate the statement, we must synthesize the conditions applying to this intersection of groups.
5
Utilize disjunctive syllogism to resolve the abatement condition.
Since the 'Plastics' option is impossible for listed corporations, the only remaining valid condition is '~Over 10M Revenue'.
When a necessary condition requires at least one of two options to be true, proving one false guarantees the other must be true.

Anahtar Kavram

Formal logic synthesis using transitive conditional chains, contrapositives, and disjunctive syllogism.
Soru 19Soru →

According to the regional agricultural board, any farmer in the valley who cultivates heirloom tomatoes must implement comprehensive pest-management protocols. Any farmer who implements comprehensive pest-management protocols is automatically disqualified from receiving the basic organic certification. Furthermore, recent records show that at least some farmers who received the newly established sustainability grant also qualified for the basic organic certification.

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

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Cevap: At least some farmers who received the newly established sustainability grant do not cultivate heirloom tomatoes.

Cevap

At least some farmers who received the newly established sustainability grant do not cultivate heirloom tomatoes.
The correct answer accurately combines the logical premises. First, we know that growing heirloom tomatoes requires comprehensive pest-management, which in turn prevents a farmer from getting the basic organic certification. Therefore, no farmer who grows heirloom tomatoes gets the certification. We also know that some farmers with the sustainability grant did get the certification. Because they got the certification, they cannot be farmers who grow heirloom tomatoes. Thus, at least some farmers with the grant do not cultivate heirloom tomatoes.

Adım Adım Çözüm

1
Diagram the first conditional statement.
Cultivates heirloom tomatoes (HT) -> Implement comprehensive pest-management (CPM).
To establish the baseline logical relationship for farmers growing heirloom tomatoes.
2
Diagram the second conditional statement and connect it to the first.
CPM -> Disqualified from basic organic certification (~BOC). Therefore, HT -> ~BOC.
Transitive property of conditional logic allows chaining statements with a shared term.
3
Diagram the third statement involving the quantifier 'some'.
Sustainability grant (SG) <-Some-> Qualifies for basic organic certification (BOC).
To integrate the quantified factual premise with the conditional chain.
4
Combine the 'some' statement with the contrapositive of the conditional chain.
Since SG <-Some-> BOC, and the contrapositive of the chain is BOC -> ~HT, it must be true that SG <-Some-> ~HT.
When 'Some A are B' and 'All B are C', it logically follows that 'Some A are C'.

Anahtar Kavram

Chaining Conditional Statements with Quantifiers
Soru 20Soru →

Recent studies on urban noise pollution have demonstrated that in metropolitan areas, prolonged exposure to traffic noise exceeding 70 decibels significantly correlates with an increased incidence of stress-related cardiovascular conditions. However, the installation of acoustic barriers along major highways only reduces noise levels by an average of 5 decibels. Furthermore, in districts where speed limits were reduced from 50 mph to 30 mph, average traffic noise dropped by over 12 decibels. Curiously, the districts that implemented both acoustic barriers and speed limit reductions experienced no greater decrease in average traffic noise than those that only reduced speed limits.

Which one of the following is most strongly supported by the information above?

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Cevap: The noise reduction effects of acoustic barriers and speed limit reductions are not entirely cumulative when both are implemented in a district.

Cevap

The noise reduction effects of acoustic barriers and speed limit reductions are not entirely cumulative when both are implemented in a district.
The stimulus establishes that speed limit reductions alone decrease noise by over 12 decibels, while combining them with acoustic barriers yields no greater decrease than the speed limit reduction alone. If the effects were fully cumulative, the combined reduction would be expected to be over 17 decibels. Because this does not occur, it is strongly supported that their individual noise reduction benefits do not fully add up when implemented together.

Adım Adım Çözüm

1
Analyze the individual effects of each noise reduction intervention.
Acoustic barriers yield an average 5 decibel reduction; reducing speed limits yields a greater than 12 decibel reduction.
Establishing the baseline effectiveness of each method is necessary to evaluate what happens when they are combined.
2
Examine the outcome when both interventions are implemented simultaneously.
Districts using both methods saw no greater noise decrease than those using only the speed limit reduction (i.e., a drop of over 12 decibels).
This comparative data point is the key premise that must be reconciled with the individual reduction numbers.
3
Synthesize the findings to derive a logically proven statement.
Because the combined effect (roughly 12+ decibels) is less than the sum of their individual effects (roughly 17+ decibels), the benefits are not fully additive.
A 'Most Strongly Supported' answer must be a direct mathematical or logical consequence of the provided premises.

Anahtar Kavram

Synthesizing premise information to identify an unstated but logically required outcome regarding overlapping variables.
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