Examkin

Inference and Deduction

215 soru

Tüm türler215Çoktan seçmeli112Çoklu seçim29Doğru / Yanlış39Eşleştirme21Sıralama14
Soru 101Soru →

Every regulatory framework adopted by the Central Trade Guild requires member states to submit quarterly audit reports. Any regulatory framework that requires quarterly audit reports also strictly restricts speculative commodity trading. Most regulatory frameworks that restrict speculative commodity trading face opposition from the agricultural coalition. However, none of the regulatory frameworks drafted by the Eastern Bloc restrict speculative commodity trading. Yet, some of the frameworks facing opposition from the agricultural coalition were drafted by the Eastern Bloc.

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: At least one regulatory framework facing opposition from the agricultural coalition does not restrict speculative commodity trading.; None of the regulatory frameworks adopted by the Central Trade Guild were drafted by the Eastern Bloc.

Cevap

The correct statements are that at least one regulatory framework facing opposition from the agricultural coalition does not restrict speculative commodity trading, and that none of the regulatory frameworks adopted by the Central Trade Guild were drafted by the Eastern Bloc.
The correct options represent the two definitively provable mathematical realities from the stimulus. First, because every Central Trade Guild framework restricts trading, and no Eastern Bloc framework restricts trading, these two categories are mutually exclusive. Second, because some frameworks facing opposition are Eastern Bloc, and all Eastern Bloc frameworks fail to restrict trading, there must exist at least one opposed framework that fails to restrict trading.

Adım Adım Çözüm

1
Diagram the conditional statements provided in the first half of the stimulus.
CTG → QAR, and QAR → RST. Through the transitive property, we can deduce CTG → RST.
Identifying absolute rules allows us to establish the necessary conditions for any framework adopted by the Central Trade Guild.
2
Diagram the remaining conditional and quantified statements.
RST -most→ OAC. EB → ~RST. OAC -some→ EB.
Mapping all relationships is required to find points of intersection and valid deductions.
3
Combine the absolute conditional chains to test relationships between distant variables.
Since CTG → RST, and EB → ~RST (which contraposes to RST → ~EB), we can deduce that CTG → ~EB. Therefore, no CTG frameworks are EB frameworks.
Linking conditional statements via their shared terms and contrapositives reveals absolute truths not explicitly stated.
4
Evaluate the quantifier relationships to find existential truths.
We know OAC -some→ EB. We also know EB → ~RST. Therefore, there must be at least one framework that is both OAC and ~RST (OAC -some→ ~RST).
When a 'some' statement intersects with an 'all' or 'none' statement, a new 'some' deduction can be definitively mathematically proven.
5
Compare the derived deductions against the given options.
The deduction 'CTG → ~EB' matches one of the correct options, and 'OAC -some→ ~RST' matches the other.
Must Be True questions require selecting answers that are 100% logically proven by the premises.

Anahtar Kavram

Must Be True Questions
Tahmini Süre:3m 0s
Soru 102Soru →

Match each of the following culinary certification rules to its correct logical contrapositive diagram.

Assume the following variables:
MM = Master status is achieved
TT = Technique is perfected
FF = Final exam is passed
EE = Critical error occurs

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Öğeler

Master status is achieved only if the technique is perfected.
Failing to perfect the technique ensures that the final exam is failed.
The final exam is passed unless a critical error occurs.
No master status is achieved without passing the final exam.

Eşleşmeler

Cevabı ve açıklamayı göster

Cevap

The correct matches require translating each English conditional statement into its baseline logical diagram, and then finding the logically equivalent contrapositive for each among the choices.
Each correct match pairs the original English statement with its logically equivalent contrapositive. By successfully identifying the sufficient and necessary conditions encoded in terms like 'only if', 'ensures', 'unless', and 'no... without', you derive the correct baseline diagram. Negating and reversing both terms then yields the provided answers.

Adım Adım Çözüm

1
Translate rule 1 and find its contrapositive.
'Master status is achieved only if the technique is perfected' translates to M→TM \rightarrow T. The contrapositive is ∼T→∼M\sim T \rightarrow \sim M.
The phrase 'only if' always precedes the necessary condition.
2
Translate rule 2 and find its contrapositive.
'Failing to perfect the technique ensures that the final exam is failed' translates to ∼T→∼F\sim T \rightarrow \sim F. The contrapositive is F→TF \rightarrow T.
The word 'ensures' functions as a sufficient condition indicator.
3
Translate rule 3 and find its contrapositive.
'The final exam is passed unless a critical error occurs' translates to ∼E→F\sim E \rightarrow F. The contrapositive is ∼F→E\sim F \rightarrow E.
The word 'unless' is logically equivalent to 'if not', negating the other term to form the sufficient condition.
4
Translate rule 4 and find its contrapositive.
'No master status is achieved without passing the final exam' translates to M→FM \rightarrow F. The contrapositive is ∼F→∼M\sim F \rightarrow \sim M.
The formula 'No X without Y' means that Y is required for X, thus X is the sufficient condition and Y is the necessary condition.

Anahtar Kavram

Translating diverse conditional language into logical symbols and recognizing contrapositives.
Soru 103Soru →

In the Highland Reserve, every adult male deer has antlers. Furthermore, any deer with antlers sheds them during the winter season. Some adult male deer in the Highland Reserve are currently tagged with tracking collars.

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: Every adult male deer in the Highland Reserve sheds its antlers during the winter season.; At least some deer in the Highland Reserve that are tagged with tracking collars shed their antlers during the winter season.

Cevap

The statements that must be true are: 'Every adult male deer in the Highland Reserve sheds its antlers during the winter season' and 'At least some deer in the Highland Reserve that are tagged with tracking collars shed their antlers during the winter season'.
The correct statements are derived from strict logical deductions. The first is a direct transitive chain: if A implies B, and B implies C, then A implies C. Since all adult male deer have antlers, and all deer with antlers shed them, all adult male deer must shed them. The second applies a subset characteristic: since some tagged deer are adult males, and all adult males shed their antlers, those specific tagged deer must also shed their antlers.

Adım Adım Çözüm

1
Analyze the conditional premises
Premise 1: Adult male deer -> has antlers. Premise 2: Has antlers -> sheds them during winter.
Identifying the formal logic relationships is the first step to finding valid deductions.
2
Chain the conditional premises
Adult male deer -> sheds them during winter.
Since 'has antlers' is the necessary condition for the first premise and the sufficient condition for the second, the two statements can be linked to form a new valid deduction.
3
Analyze the quantifier premise
Premise 3: Some adult male deer are tagged with tracking collars.
To find further deductions, we must combine the 'some' statement with the universal conditional statements.
4
Combine the quantifier with the conditional chain
Since at least some adult male deer are tagged, and all adult male deer shed their antlers during winter, it must be true that some tagged deer shed their antlers during winter.
When a subgroup (some tagged deer) belongs to a larger group (adult male deer) that shares a universal characteristic (sheds antlers), that subgroup must also share the characteristic.

Anahtar Kavram

Conditional logic chaining and quantifier intersection
Soru 104Soru →

Under the new municipal regulations, any local business that fails the annual safety inspection is heavily fined and subjected to a mandatory operational audit. Some local businesses that are subjected to a mandatory operational audit receive municipal tax grants. However, no local business that receives a municipal tax grant has ever been heavily fined.

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

Cevabı ve açıklamayı göster

Cevap: A local business that receives a municipal tax grant failed the annual safety inspection.

Cevap

The statement that a local business receiving a municipal tax grant failed the annual safety inspection cannot be true.
Based on the stimulus, failing the safety inspection guarantees a heavy fine. However, receiving a municipal tax grant guarantees that a business is NOT heavily fined. Therefore, these two conditions are mutually exclusive. It is logically impossible for a business to both fail the inspection and receive a tax grant.

Adım Adım Çözüm

1
Translate the premises into logical notation.
1. Fails Inspection -> Heavily Fined AND Mandatory Audit. 2. Mandatory Audit 'some' Tax Grant. 3. Tax Grant -> NOT Heavily Fined.
Formalizing the logic prevents confusion when combining statements and checking inferences.
2
Combine the first and third premises using the shared variable 'Heavily Fined'.
Fails Inspection -> Heavily Fined. The contrapositive of the third premise is: Heavily Fined -> NOT Tax Grant. Connecting them yields: Fails Inspection -> NOT Tax Grant.
Connecting conditionals reveals the implicit constraints that dictate what is logically impossible.
3
Evaluate the options against the deduced chain.
The option stating a business receives a grant and fails the inspection directly contradicts the deduction that failing the inspection guarantees NOT receiving a grant.
In a 'Cannot Be True' question, the correct answer must violate a stated premise or a valid deduction.

Anahtar Kavram

Cannot Be True Questions
Soru 105Soru →

At Vance Corporation, every employee who holds a Level 3 security clearance must complete a quarterly cybersecurity training module. Furthermore, any employee who completes the quarterly cybersecurity training module is eligible for the remote work program.

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

Cevabı ve açıklamayı göster

Cevap: Every employee at Vance Corporation who holds a Level 3 security clearance is eligible for the remote work program.

Cevap

Every employee at Vance Corporation who holds a Level 3 security clearance is eligible for the remote work program.
The correct answer accurately combines the two conditional statements provided in the stimulus. If every employee with a Level 3 clearance completes the training, and everyone who completes the training is eligible for remote work, it logically follows that every employee with a Level 3 clearance is eligible for remote work. This is a flawless transitive deduction.

Adım Adım Çözüm

1
Diagram the first conditional premise.
Level 3 clearance -> Must complete training.
The phrase 'every employee who holds...' introduces a sufficient condition.
2
Diagram the second conditional premise.
Completes training -> Eligible for remote work.
The phrase 'any employee who...' introduces a sufficient condition.
3
Combine the conditional statements to form a deductive chain.
Level 3 clearance -> Must complete training -> Eligible for remote work.
The necessary condition of the first premise is identical to the sufficient condition of the second premise.
4
Evaluate the new inference.
Therefore, if an employee has a Level 3 clearance, they are guaranteed to be eligible for the remote work program.
This directly matches the correct option, proving it is 100% true based solely on the text.

Anahtar Kavram

Chaining Conditional Statements
Soru 106Soru →

Consider the following premises:
All certified lifeguards at Ocean Beach must be able to swim a mile in under 20 minutes. Only individuals who have completed the advanced water rescue course are certified lifeguards at Ocean Beach.

Based on these premises, the scenario in which an individual is a certified lifeguard at Ocean Beach without having completed the advanced water rescue course cannot be true.

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True
The evaluation is true. The premises establish that completing the rescue course is a strict necessary condition for being a lifeguard. A scenario that claims someone is a lifeguard without having taken the course directly violates this condition, meaning the scenario logically cannot be true.

Adım Adım Çözüm

1
Analyze the conditional statements in the premises.
The key premise is 'Only individuals who have completed the advanced water rescue course are certified lifeguards at Ocean Beach.'
Identifying formal logic relationships is necessary to determine what is and isn't logically possible.
2
Translate the key premise into a formal conditional relationship.
The word 'only' introduces the necessary condition. Translation: If an individual is a certified lifeguard (sufficient condition), then they must have completed the advanced water rescue course (necessary condition).
Standardizing the logic prevents misinterpretation of sufficient and necessary conditions.
3
Evaluate the proposed scenario against the conditional relationship.
The scenario proposes someone is a certified lifeguard (sufficient condition met) but has NOT completed the course (necessary condition not met).
A scenario cannot logically exist if it affirms a sufficient condition but denies its absolute necessary requirement.
4
Determine the truth value of the evaluation statement.
Since the scenario directly contradicts the established premises, it indeed cannot be true. Therefore, the statement claiming the scenario cannot be true is accurate.
Finalizing the logical deduction to directly answer the prompt.

Anahtar Kavram

Identifying logically impossible scenarios based on strict conditional reasoning and necessary conditions introduced by the word 'only'.
Soru 107Soru →

Under the new municipal zoning code, obtaining a commercial building permit requires that the developer submit a comprehensive environmental impact report and secure approval from the local neighborhood council.

Which one of the following statements logically follows from the zoning code requirements?

Cevabı ve açıklamayı göster

Cevap: If a developer fails to secure approval from the local neighborhood council, they will not obtain a commercial building permit, even if they have submitted a comprehensive environmental impact report.

Cevap

The correct answer states that failing to secure approval from the local neighborhood council guarantees the developer will not obtain a commercial building permit, even if the other requirement is met.
The stimulus establishes a rule where obtaining a permit requires two separate necessary conditions: submitting a report AND getting council approval. According to formal logic, if a sufficient condition requires a compound necessary condition (A -> B and C), the contrapositive dictates that failing either necessary condition guarantees the sufficient condition cannot occur (~B or ~C -> ~A). Therefore, a developer who fails to get council approval will definitively not get a permit, regardless of whether they submitted the report.

Adım Adım Çözüm

1
Identify the conditional relationship in the stimulus.
Obtaining a permit (Sufficient) -> Submit environmental report AND secure council approval (Necessary).
The phrase 'requires that' introduces necessary conditions for the event that precedes it.
2
Form the contrapositive using De Morgan's laws.
If a developer does NOT submit the report OR does NOT secure council approval -> they will NOT obtain a permit.
To create a valid contrapositive, negate both sides and reverse their order. When negating an 'AND' statement, it becomes an 'OR' statement.
3
Evaluate the answer choices against the deduced contrapositive.
The correct choice matches one half of the 'OR' condition in the contrapositive.
Because failing either one of the necessary conditions is sufficient to prevent obtaining the permit, lacking council approval guarantees denial of the permit.

Anahtar Kavram

Forming contrapositives from compound conditional statements (De Morgan's Laws).
Soru 108Soru →

Any municipality that adopts the Comprehensive Water Management protocol must install smart meters in all its commercial buildings. Installing smart meters in all commercial buildings guarantees that a municipality will demonstrate a reduction in peak usage rates. Furthermore, a municipality cannot secure a Regional Infrastructure Grant unless it demonstrates a reduction in peak usage rates. Most municipalities in the Arid Basin region have adopted the Comprehensive Water Management protocol. However, most municipalities in the Arid Basin region failed to secure a Regional Infrastructure Grant.

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

Cevabı ve açıklamayı göster

Cevap: At least some municipalities that demonstrated a reduction in peak usage rates failed to secure a Regional Infrastructure Grant.

Cevap

At least some municipalities that demonstrated a reduction in peak usage rates failed to secure a Regional Infrastructure Grant.
The stimulus establishes that adopting the protocol guarantees a reduction in peak usage rates. Since most municipalities in the Arid Basin adopted the protocol, it must be true that most municipalities in the Arid Basin demonstrated this reduction. The stimulus also explicitly states that most municipalities in the Arid Basin failed to secure a grant. Whenever 'most' (more than 50%) of a specific group has property X, and 'most' of that same group has property Y, there must be at least some overlap between the two subgroups. Therefore, there must be at least some municipalities that have both demonstrated the reduction and failed to secure the grant.

Adım Adım Çözüm

1
Diagram the absolute conditional statements established in the stimulus.
Protocol → Smart Meters; Smart Meters → Reduction; Grant → Reduction.
This establishes the necessary and sufficient relationships, allowing us to chain the first two rules: Protocol → Reduction.
2
Analyze the quantifier statements applying to the Arid Basin region.
Arid Basin (most) → Protocol. Arid Basin (most) → No Grant.
Tracking these group-specific quantities is essential for finding overlapping characteristics.
3
Combine the quantifier statements with the established conditional chain.
Because 'Arid Basin (most) → Protocol' and 'Protocol → Reduction', it follows logically that 'Arid Basin (most) → Reduction'.
A conditional rule applies to any member of a group that meets the sufficient condition.
4
Synthesize the two resulting majorities for the Arid Basin region.
More than half of the Arid Basin municipalities demonstrated a Reduction, and more than half of the Arid Basin municipalities received No Grant.
When two 'most' statements apply to the exact same finite group, they must mathematically intersect. Therefore, there is at least one municipality with both characteristics (Reduction AND No Grant).

Anahtar Kavram

Combining formal conditional chains with overlapping logical quantifiers (the 'Most + Most = Some' intersection rule).

Alternatif Yöntem

You can visualize this mathematically: If there are 100 municipalities in the Arid Basin, 'most' means at least 51. So, at least 51 achieved a reduction. At the same time, at least 51 failed to secure a grant. 51 + 51 = 102, which is greater than 100. This mathematically proves that at least 2 municipalities must fall into both categories.
Tahmini Süre:2m 0s
Soru 109Soru →

A maritime arbitration board relies on a strict set of regulations to determine the obligations and reimbursements for salvage operations.

You are given the initial premise: 'The cargo of the salvaged vessel is classified as containing hazardous materials.'
Your goal is to logically deduce the conclusion: 'The operation's costs will not be fully reimbursed by the state fund.'

Arrange the following regulatory rules in the exact logical sequence required to form an unbroken deductive chain from the given premise to the target conclusion.

Öğeleri doğru sıraya koymak için sürükleyin

Cevabı ve açıklamayı göster

Cevap

The correct logical sequence translates the rules to form the chain: Hazardous Materials → EPA Registration → Auditor Deployed → Bond Posted → Mandatory Audit → Costs Not Reimbursed.
To build the deductive chain, each rule must be translated accurately into formal logic to connect the necessary condition of one rule to the sufficient condition of the next. The sequence begins with the premise 'Hazardous Materials' (HM). The rule 'Cannot be HM unless EPA' translates to HM → EPA. Next, 'Unless Auditor, cannot be EPA' translates to EPA → Auditor. Then, 'Prerequisite for Auditor is Bond' translates to Auditor → Bond. 'Any Bond is Audit' translates to Bond → Audit. Finally, 'For Reimbursed, must not Audit' translates to Reimbursed → Not Audit, whose contrapositive is Audit → Not Reimbursed. Chaining these yields: HM → EPA → Auditor → Bond → Audit → Not Reimbursed. Applying the premise HM, the conclusion Not Reimbursed validly follows in this exact sequence.

Adım Adım Çözüm

1
Translate the rule containing the initial premise (Hazardous Materials).
rule_hm_epa translates to: Hazardous Materials → EPA Registration.
The phrase 'cannot be X unless Y' means if not Y, then not X (contrapositive: X → Y).
2
Find the rule triggered by EPA Registration.
rule_epa_iea translates to: EPA Registration → Auditor Deployed.
The phrase 'Unless X, cannot be Y' means if not X, then not Y (contrapositive: Y → X).
3
Find the rule triggered by Auditor Deployed.
rule_iea_sib translates to: Auditor Deployed → Bond Posted.
A 'prerequisite' is a necessary condition. If the auditor is deployed (sufficient condition met), the prerequisite must have been satisfied.
4
Find the rule triggered by Bond Posted.
rule_sib_lca translates to: Bond Posted → Mandatory Audit.
'Any X is Y' introduces a straightforward sufficient → necessary relationship.
5
Find the rule connecting Mandatory Audit to the final conclusion (Costs Not Reimbursed).
rule_lca_reimburse translates to: Costs Reimbursed → Not Audit. Contrapositive: Mandatory Audit → Costs Not Reimbursed.
Applying the contrapositive of this requirement completes the deductive chain to the target conclusion.

Anahtar Kavram

Conditional logic translation and deductive chaining
Tahmini Süre:2m 30s
Soru 110Soru →

Under the new oceanographic regulations, any mining corporation that holds a Deepwater Extraction Permit must submit an annual benthic ecosystem report to the regulatory commission. Any corporation that submits an annual benthic ecosystem report is authorized to operate autonomous dredging vehicles. However, no corporation that is authorized to operate autonomous dredging vehicles can qualify for the marine conservation tax credit. Furthermore, most mining corporations currently operating in the Abyssal Sector hold a Deepwater Extraction Permit.

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

Geçerli olan tümünü seçin

Cevabı ve açıklamayı göster

Cevap: Any mining corporation that qualifies for the marine conservation tax credit does not hold a Deepwater Extraction Permit.; Most mining corporations currently operating in the Abyssal Sector do not qualify for the marine conservation tax credit.

Cevap

The correct statements are that any corporation qualifying for the tax credit lacks a permit, and that most corporations in the Abyssal Sector do not qualify for the tax credit.
The correct options are logically proven by the text. The first correct option relies on the contrapositive of the stimulus rules: since holding a permit strictly guarantees losing the tax credit, qualifying for the credit guarantees a corporation does not hold a permit. The second correct option relies on chaining a quantifier with a universal rule: since most Abyssal Sector corporations hold a permit, and all permit holders lose the credit, most Abyssal Sector corporations lose the credit.

Adım Adım Çözüm

1
Diagram the universal conditional statements provided in the stimulus.
Permit -> Report; Report -> Vehicles; Vehicles -> NOT Tax Credit.
To establish the formal logical chain linking the distinct corporate requirements and restrictions.
2
Chain the universal conditionals together and form their contrapositive.
Chain: Permit -> Report -> Vehicles -> NOT Tax Credit. Contrapositive: Tax Credit -> NOT Vehicles -> NOT Report -> NOT Permit.
Deductions in Must Be True questions frequently rely on valid conditional chains and their contrapositives.
3
Diagram the quantifier statement and integrate it with the universal chain.
Abyssal Sector -most-> Permit. Linking this to the chain: Abyssal Sector -most-> Permit -> NOT Tax Credit. Therefore, Abyssal Sector -most-> NOT Tax Credit.
Formal logic permits applying a universal conditional to a subset defined by a 'most' statement.
4
Evaluate the answer choices strictly against these proven deductions.
The option stating 'Tax Credit -> NOT Permit' matches the contrapositive chain. The option stating 'Abyssal Sector -most-> NOT Tax Credit' matches the integrated quantifier chain. The remaining options represent classic formal logic errors.
Correct options in standard Must Be True questions must be 100% provable without any outside assumptions.

Anahtar Kavram

Chaining formal conditional statements, forming contrapositives, and applying quantifiers to universal rules.
Soru 111Soru →

Any commercial aircraft manufactured by AeroStar is equipped with the new Zenith navigation system. An aircraft requires a specialized maintenance team on site to undergo its routine inspections if it is equipped with the Zenith navigation system. The municipal airport in Grandville does not have any specialized maintenance teams on site.

Based on these statements, the following scenario cannot be true: A commercial aircraft manufactured by AeroStar undergoes a routine inspection at the municipal airport in Grandville.

Cevabı ve açıklamayı göster

Cevap: True

Cevap

The statement is true because the provided scenario is logically impossible based on the given conditional rules.
The scenario directly contradicts the deduced contrapositive. Since any AeroStar aircraft requires a specialized team on site, and Grandville does not have one, the event cannot occur.

Adım Adım Çözüm

1
Map the first two conditional statements to form a chain.
AeroStar aircraft -> Zenith system. Zenith system -> specialized maintenance team on site. Combined: AeroStar aircraft -> specialized maintenance team on site.
Linking conditional statements is the standard method for determining what must be true or what cannot be true in deductive logic.
2
Apply the contrapositive using the information about Grandville.
Grandville airport -> NO specialized maintenance team on site. Therefore, NO Zenith system, which means NOT an AeroStar aircraft undergoing inspection.
The definitive absence of a necessary condition guarantees the absence of the sufficient conditions that rely upon it.
3
Evaluate the proposed scenario against the deductive proof.
The scenario places an AeroStar aircraft undergoing a routine inspection at a location that strictly cannot support it, creating a direct contradiction.
A scenario that contradicts a valid deductive inference drawn from the premises cannot be true.

Anahtar Kavram

Cannot Be True Questions
Soru 112Soru →

According to international maritime records, any commercial vessel constructed after 2020 that is equipped with a dual-fuel engine is certified for zero-emission operations. Furthermore, no vessel is certified for zero-emission operations unless it utilizes a purely electric auxiliary power system. However, there are no commercial vessels built before 2025 that utilize purely electric auxiliary power systems.

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

Cevabı ve açıklamayı göster

Cevap: A commercial vessel constructed in 2024 is equipped with a dual-fuel engine.

Cevap

The statement that a commercial vessel constructed in 2024 is equipped with a dual-fuel engine cannot be true, as it creates an impossible set of requirements.
Based on the rules provided, a commercial vessel constructed after 2020 with a dual-fuel engine absolutely must have a purely electric auxiliary power system. However, the final rule strictly forbids any commercial vessel built before 2025 from having this system. Therefore, any commercial vessel constructed in 2021, 2022, 2023, or 2024 is logically prohibited from having a dual-fuel engine.

Adım Adım Çözüm

1
Translate the first premise into conditional logic.
Commercial Vessel AND Constructed After 2020 AND Dual-Fuel Engine → Certified for Zero-Emission.
This establishes the sufficient condition that triggers the certification requirement.
2
Translate the second premise and link it to the first.
Certified for Zero-Emission → Purely Electric Auxiliary System. Therefore, Post-2020 Commercial Dual-Fuel → Purely Electric Auxiliary System.
The word 'unless' introduces a necessary condition, allowing us to form a deductive chain.
3
Analyze the third premise (the constraint).
Commercial Vessel AND Constructed Before 2025 → NOT (Purely Electric Auxiliary System).
This sets a hard boundary on when a commercial vessel can possess the electric system.
4
Evaluate the overlap between the deductive chain and the constraint.
A commercial vessel built between 2021 and 2024 with a dual-fuel engine MUST have an electric system (Step 2) but CANNOT have an electric system (Step 3).
Identifying the overlapping years (after 2020, but before 2025) reveals the logical impossibility that answers the 'Cannot Be True' question.

Anahtar Kavram

Identifying a scenario that violates the necessary conclusion of a chained conditional statement combined with a categorical restriction.
Tahmini Süre:1m 45s
Soru 113Soru →

Consider the following stimulus:

Last year, the city of Oakhaven implemented a new recycling program that accepts a wider variety of plastics than the previous program. Since the implementation of this new program, the total volume of trash sent to Oakhaven's landfill has decreased by 15%, even though the city's population has remained constant and overall consumption patterns have not changed.

Statement: Based on the information provided, it is most strongly supported that Oakhaven's new recycling program is at least partially responsible for the decrease in the volume of trash sent to the landfill.

Cevabı ve açıklamayı göster

Cevap: True

Cevap

The statement is True. The stimulus strongly supports the inference that the recycling program contributed to the reduction in landfill trash.
The correct answer is True because the premises establish a clear temporal relationship between the new program and the decrease in trash, while explicitly eliminating key alternative causes (population and consumption changes). This synthesis strongly supports the causal inference.

Adım Adım Çözüm

1
Analyze the premises provided in the stimulus.
The city expanded its recycling program, landfill trash decreased by 15%, and both population and consumption patterns remained constant.
To establish the factual evidence that can be used to support an inference.
2
Evaluate the given statement against the premises.
The statement claims there is a likely causal link between the new recycling program and the decrease in trash.
To determine if the statement represents a strongly supported inference.
3
Assess the strength of the logical support.
Because alternative explanations (population change, consumption change) are explicitly ruled out, the introduction of the recycling program is the most logical and highly supported cause presented for the decrease.
To verify if the statement meets the threshold of being 'most strongly supported'.

Anahtar Kavram

Synthesizing premises to evaluate a strongly supported causal inference.
Soru 114Soru →

The logically valid contrapositive of the statement 'A clinical trial is deemed ethically sound only if it obtains informed consent from all participants and minimizes potential risks' is 'If a clinical trial fails to obtain informed consent from all participants or fails to minimize potential risks, then it is not deemed ethically sound.'

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True
The original statement translates to 'If a trial is ethically sound, then it has informed consent AND minimized risks.' Forming the contrapositive requires reversing the conditions and negating them. According to De Morgan's laws, negating an 'AND' statement turns it into an 'OR' statement. Therefore, 'If it does not have informed consent OR does not minimize risks, then it is not ethically sound' is the exact logically valid contrapositive.

Adım Adım Çözüm

1
Identify the sufficient and necessary conditions in the original statement.
Sufficient: A clinical trial is deemed ethically sound. Necessary: It obtains informed consent from all participants AND minimizes potential risks.
The phrase 'only if' introduces necessary conditions, while the subject of the sentence acts as the sufficient condition.
2
Formulate the logical relationship of the original statement.
Ethically sound -> (Informed consent AND Minimizes risks)
To apply formal logic rules accurately, we must translate the English text into conditional notation.
3
Apply the rule of contraposition and De Morgan's laws.
NOT (Informed consent AND Minimizes risks) -> NOT Ethically sound. This simplifies to: (NOT Informed consent OR NOT Minimizes risks) -> NOT Ethically sound.
The contrapositive requires negating and reversing both sides. Negating an 'AND' statement requires changing it to an 'OR' statement.
4
Compare the resulting logical formulation to the proposed contrapositive in the stem.
The proposed contrapositive matches the derived logical formulation perfectly.
To determine if the statement is true, the proposed text must reflect the exact logical equivalent.

Anahtar Kavram

Forming Contrapositives with Compound Conditionals
Soru 115Soru →

Consider the following statements:

Any researcher who directs a Phase III clinical trial must hold both a board certification in immunology and a minimum of ten years of clinical practice.
Unless a researcher has published a peer-reviewed virology study, they cannot obtain a board certification in immunology.
Most researchers with a minimum of ten years of clinical practice have never published a peer-reviewed virology study.
Dr. Aris is currently directing a Phase III clinical trial.

Based on these statements, the claim that 'Dr. Aris belongs to the majority of researchers with at least ten years of clinical practice who have never published a peer-reviewed virology study' cannot be true.

Cevabı ve açıklamayı göster

Cevap: True

Cevap

True. The provided claim explicitly contradicts the valid deductive chain derived from the premises, meaning it genuinely cannot be true.
The statement accurately identifies that the internal claim is logically impossible. Dr. Aris directing a trial guarantees he has a board certification, which in turn guarantees he has published a virology study. The claim that he belongs to the majority who have never published this study directly contradicts this proven fact.

Adım Adım Çözüm

1
Map the conditional statements provided in the premises.
Directing Trial -> Board Certification AND 10+ Years Practice. Board Certification -> Published Virology Study.
Translating formal logic into a deductive chain is required to track necessary conditions.
2
Apply the conditional chain to the specific subject, Dr. Aris.
Because Dr. Aris is directing a trial, he must have 10+ years of practice AND a Board Certification. Consequently, he must have a Published Virology Study.
This establishes the undeniable facts about Dr. Aris.
3
Evaluate the quantitative statement regarding researchers with 10+ years of practice.
Most (the majority) do NOT have a published study. Therefore, those who DO have a published study make up the minority of this group.
This defines the demographic groups mentioned in the target claim.
4
Compare Dr. Aris's deduced characteristics against the target claim.
The claim places Dr. Aris in the majority (those who have NEVER published the study). The deduction proves Dr. Aris HAS published the study (placing him in the minority).
Identifying this direct contradiction confirms that the claim is logically impossible.

Anahtar Kavram

Conditional Logic Chaining and Subgroup Quantifiers
Tahmini Süre:2m 0s
Soru 116Soru →

According to the newly adopted protocols by the Ministry of Health, a pharmaceutical company is permitted to bypass the standard three-phase clinical trial only if the medication in question targets a designated rare disease or has already received full regulatory approval in a recognized partner nation.

Which one of the following logically follows from the Ministry of Health's protocols?

Cevabı ve açıklamayı göster

Cevap: If a medication neither targets a designated rare disease nor has received full regulatory approval in a recognized partner nation, then the pharmaceutical company is not permitted to bypass the standard three-phase clinical trial.

Cevap

If a medication neither targets a designated rare disease nor has received full regulatory approval in a recognized partner nation, then the pharmaceutical company is not permitted to bypass the standard three-phase clinical trial.
This option accurately presents the logically valid contrapositive of the stimulus. The original statement is structured as: Bypass -> (Rare Disease OR Partner Approval). The contrapositive requires negating both sides and reversing the logical arrow. Crucially, by De Morgan's laws, negating a disjunction (Rare Disease OR Partner Approval) creates a conjunction (NOT Rare Disease AND NOT Partner Approval). Therefore, if a medication lacks both required criteria, the company is absolutely not permitted to bypass the clinical trials.

Adım Adım Çözüm

1
Identify the sufficient and necessary conditions in the stimulus.
Sufficient condition: permitted to bypass trials. Necessary condition: targets a rare disease OR has partner approval.
The phrase 'only if' introduces a necessary condition.
2
Formalize the conditional statement.
Bypass -> (Rare Disease OR Partner Approval)
This establishes the core logical relationship provided by the Ministry of Health's protocol.
3
Apply De Morgan's laws to form the valid contrapositive.
Negating an 'OR' statement creates an 'AND' statement. Therefore: (NOT Rare Disease AND NOT Partner Approval) -> NOT Bypass.
A valid contrapositive requires reversing the conditions and negating both sides. For compound conditionals, De Morgan's laws mandate flipping disjunctions to conjunctions.
4
Evaluate the answer choices to find the match.
The correct option perfectly reflects the deduction: neither targeting a rare disease nor having approval (NOT Rare Disease AND NOT Partner Approval) means the company is not permitted to bypass the trial.
The correct answer to a 'must be true' inference question testing conditionals is almost always the exact contrapositive.

Anahtar Kavram

Forming contrapositives of compound conditional statements using De Morgan's laws.
Tahmini Süre:1m 30s
Soru 117Soru →

Read the following information and evaluate the logical validity of the statement below.

Any climate model that predicts a complete reduction in Arctic sea ice by 2050 also assumes a rapid acceleration of oceanic warming. No climate model that assumes a rapid acceleration of oceanic warming fails to account for increased cloud cover albedo. Furthermore, only climate models that incorporate localized atmospheric pressure anomalies can accurately account for increased cloud cover albedo. An analysis of recent publications shows that several prominent climate models developed by the Global Meteorological Institute predict a complete reduction in Arctic sea ice by 2050.

Statement: Based on the information above, it must be true that most climate models developed by the Global Meteorological Institute incorporate localized atmospheric pressure anomalies.

Cevabı ve açıklamayı göster

Cevap: False

Cevap

False
The provided statement relies on an invalid quantifier escalation. By connecting the conditional rules, we can definitively prove that any model predicting a complete ice reduction must incorporate localized atmospheric pressure anomalies. Because 'several' Global Meteorological Institute (GMI) models predict this reduction, it must be true that 'some' GMI models incorporate the anomalies. However, 'several' does not mean 'most' (more than 50%), so the statement provided is an overreach and is not necessarily true.

Adım Adım Çözüm

1
Translate the first conditional premise into formal logic.
Predict Ice Reduction → Assume Rapid Acceleration.
The word 'Any' introduces a sufficient condition.
2
Translate the second conditional premise into formal logic.
Assume Rapid Acceleration → Account for Albedo.
The phrase 'No [X] fails to [Y]' creates a double negative, meaning every [X] must do [Y].
3
Translate the third conditional premise into formal logic.
Account for Albedo → Incorporate Anomalies.
The word 'only' introduces a necessary condition.
4
Combine the translated premises to form a comprehensive logical chain.
Predict Ice Reduction → Assume Rapid Acceleration → Account for Albedo → Incorporate Anomalies.
The transitive property of conditional logic allows linking shared terms.
5
Evaluate the quantifier given in the final premise regarding the specific models.
Several (Some) GMI models → Predict Ice Reduction.
To apply the formal chain to the specific subgroup discussed in the stimulus.
6
Draw the valid inference and compare it to the given statement.
Valid deduction: Some GMI models → Incorporate Anomalies. The statement claims 'most', which is an invalid escalation.
In formal logic, 'some' (at least one) does not mathematically justify 'most' (more than half).

Anahtar Kavram

Quantifier logic (translating 'several' to 'some') and recognizing unsupported magnitude escalations within complex conditional deductions.
Tahmini Süre:2m 0s
Soru 118Soru →

In the town of Greenville, a local ordinance requires that all residential buildings constructed after the year 2020 be equipped with solar panels. The Oakwood Apartment complex, a residential building in Greenville, was completed in 2022. On the other hand, the Pinecone Townhomes, another residential building in Greenville, are not equipped with solar panels.

Based on the information above, which of the following statements are most strongly supported?

Geçerli olan tümünü seçin

Cevabı ve açıklamayı göster

Cevap: The Oakwood Apartment complex is equipped with solar panels.; The Pinecone Townhomes were not constructed after the year 2020.

Cevap

The statements supported are that the Oakwood Apartment complex is equipped with solar panels, and the Pinecone Townhomes were not constructed after the year 2020.
The stimulus establishes a conditional rule: If a residential building in Greenville is constructed after 2020, it must have solar panels. The Oakwood complex meets this sufficient condition (built in 2022), so it must have solar panels. The Pinecone Townhomes lack solar panels, meaning they fail the necessary condition. By contrapositive logic, they could not have been built after 2020.

Adım Adım Çözüm

1
Identify the core conditional rule provided in the stimulus.
Rule: If a residential building in Greenville was constructed after 2020, then it is equipped with solar panels.
Establishing the main conditional statement is necessary to evaluate which inferences are logically valid.
2
Apply the conditional rule to the Oakwood Apartment complex.
Oakwood is a residential building completed in 2022 (after 2020). Therefore, it must be equipped with solar panels.
This directly applies the sufficient condition of the rule (Modus Ponens) to derive a valid conclusion.
3
Apply the conditional rule to the Pinecone Townhomes.
Pinecone is a residential building without solar panels. Therefore, it was not constructed after 2020.
This applies the contrapositive of the rule (Modus Tollens): If it does not have solar panels, it cannot have been constructed after 2020.

Anahtar Kavram

Evaluating valid inferences using conditional logic, including direct application (Modus Ponens) and the contrapositive (Modus Tollens).
Soru 119Soru →

Match each conditional cybersecurity rule from the corporate protocol manual on the left with its logically equivalent contrapositive on the right.

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Öğeler

A contractor receives elevated system privileges only if they pass a comprehensive security audit.
Deploying the emergency containment protocol requires both authorization from the director and at least two active secondary servers.
The internal communications network will remain isolated unless the external threat neutralizes.
An employee's device is flagged for immediate review if it connects to an unsecured network or downloads restricted software.

Eşleşmeler

Cevabı ve açıklamayı göster

Cevap

The correct matches pair each original statement with its exact logical contrapositive by reversing the sufficient and necessary conditions, negating both, and properly applying De Morgan's laws to compound rules.
Each correct right-side item represents a logically valid deduction from the corresponding left-side item. The contrapositive is formed by universally reversing the direction of the conditional relationship and negating both sides. When terms include 'AND' or 'OR', De Morgan's laws correctly transform the operators during the negation process.

Adım Adım Çözüm

1
Analyze the 'only if' statement regarding system privileges.
Matches with 'If a contractor does not pass a comprehensive security audit...'
'Only if' indicates a necessary condition (Privileges -> Audit). Reversing and negating yields: If not Audit, then not Privileges.
2
Analyze the compound 'requires both' statement regarding the containment protocol.
Matches with 'If director authorization is missing or there are fewer than two active secondary servers...'
The sufficient condition is deploying the protocol. The necessary condition is a conjunction (Director AND Servers). The contrapositive negates the conjunction into a disjunction (Not Director OR Not Servers).
3
Analyze the 'unless' statement regarding the communications network.
Matches with 'If the internal communications network does not remain isolated...'
'Unless' is translated as 'if not' (If not Neutralized -> Isolated). The contrapositive flips and negates this: If not Isolated -> Neutralized.
4
Analyze the compound 'if' statement regarding employee devices.
Matches with 'If an employee's device is not flagged for immediate review...'
The 'if' introduces a sufficient condition that is a disjunction (Unsecured OR Restricted -> Flagged). The contrapositive negates the disjunction into a conjunction: Not Flagged -> (Not Unsecured AND Not Restricted).

Anahtar Kavram

Forming Contrapositives and Applying De Morgan's Laws
Soru 120Soru →

A financial regulatory board has issued a new set of auditing standards. Below are four rules extracted from these standards. Match each English regulatory rule to its accurate formal logical diagram.

Use the following variables for your diagramming:
AA: The audit is approved
RR: The receipts are verified
LL: The ledger is balanced
DD: Discrepancies are reported

Soldaki öğeye tıklayın, sonra eşleşen sağdaki öğeye tıklayın

Öğeler

No audit is approved without both the receipts being verified and the ledger being balanced.
The ledger is balanced if the audit is approved, unless discrepancies are reported.
The audit being approved requires the receipts to be verified, but the ledger being balanced is sufficient for the audit to be approved.
The audit is approved if, but only if, the ledger is balanced and no discrepancies are reported.

Eşleşmeler

Cevabı ve açıklamayı göster

Cevap

The correct matches are:
'No audit is approved without both...' matches with A→(R∧L)A \rightarrow (R \land L)
'The ledger is balanced if the audit is approved, unless...' matches with A→(L∨D)A \rightarrow (L \lor D)
'The audit being approved requires the receipts...' matches with (A→R)∧(L→A)(A \rightarrow R) \land (L \rightarrow A)
'The audit is approved if, but only if...' matches with A↔(L∧¬D)A \leftrightarrow (L \land \neg D)
Each statement successfully maps English syntactic cues to their formal propositional logic equivalents. Mastering the nuances of words like 'unless', 'only if', and 'requires' ensures you avoid illegal reversals or negations in deduction chains.

Adım Adım Çözüm

1
Analyze the first statement for necessary conditions.
Translates 'No X without Y' to X -> Y, resulting in A -> (R AND L).
The 'without' modifier establishes that the absence of R and L precludes A, meaning A firmly implies their presence.
2
Deconstruct the 'unless' clause in the second statement.
Translates to ~D -> (A -> L), which is logically equivalent to A -> (L OR D).
'Unless' negates the following condition to form the sufficient trigger. Distributing this across the nested conditional yields an 'OR' relationship on the necessary side.
3
Split the third statement into its 'requires' and 'sufficient' components.
Yields two separate conditionals: A -> R and L -> A.
The sentence explicitly divides the relationship between R being necessary for A, and L being sufficient to guarantee A.
4
Identify the biconditional indicator in the fourth statement.
Translates 'if, but only if' to a two-way arrow, resulting in A <-> (L AND ~D).
Biconditionals indicate that both sides of the relationship are simultaneously necessary and sufficient for each other.

Anahtar Kavram

Accurate formal logical translation of complex English indicators ('unless', 'no X without Y', 'requires', 'sufficient', 'if, but only if').
Tahmini Süre:2m 30s
ÖncekiSayfa 6 / 11Sonraki
Inference and Deduction Alıştırma Soruları — LSAT — Sayfa 6 | Examkin