A researcher claims that all patients with symptom X have disease Y. If a patient has disease Y but no symptom X, what does this indicate about the researcher's claim?

The claim is invalid because the presence of Y without X contradicts it.

The claim is strengthened as Y can exist without X.

The claim remains unaffected since Y's presence isn't linked to X.

The claim is automatically confirmed by this observation.

If all A are B and some B are C, which conclusion is logically valid?

Not enough information to conclude.

Given: 'If a country has high GDP, it will have low crime. Country X has high GDP.' What logically follows?

GDP and crime are unrelated in this case.

Country X's crime rate cannot be determined.

A teacher states: 'Students who score above 90% will get an A. Maria scored 88%.' What valid conclusion can be drawn?

The grading criteria are flawed.

If 'All metals conduct electricity' and 'Copper is a metal', what conclusion logically follows?

Not all metals conduct electricity.

HEC HAT-1 (Engineering / IT / Math / Physics) analytical reasoning Critical Thinking Set 2

HEC HAT-1 (Engineering / IT / Math / Physics) analytical reasoning Critical Thinking — Set 2

Question 1
Q1. A researcher claims that all patients with symptom X have disease Y. If a patient has disease Y but no symptom X, what does this indicate about the researcher's claim?
- A) The claim is invalid because the presence of Y without X contradicts it.
- B) The claim is strengthened as Y can exist without X.
- C) The claim remains unaffected since Y's presence isn't linked to X.
- D) The claim is automatically confirmed by this observation.
Answer: The claim is invalid because the presence of Y without X contradicts it.
Explanation: A. The claim requires X to always imply Y. Presence of Y without X doesn't disprove it, but presence of X without Y would. B fails because Y without X doesn't support the claim.
Question 2
Q2. If all A are B and some B are C, which conclusion is logically valid?
- A) All A are C.
- B) Some A are C.
- C) No A are C.
- D) Not enough information to conclude.
Answer: Not enough information to conclude.
Explanation: D. The premises don't establish a direct A-C relationship. A/B/C are invalid because they assume connections not supported by 'some' and 'all' overlap.
Question 3
Q3. Given: 'If a country has high GDP, it will have low crime. Country X has high GDP.' What logically follows?
- A) Country X has low crime.
- B) Country X has high crime.
- C) GDP and crime are unrelated in this case.
- D) Country X's crime rate cannot be determined.
Answer: Country X has low crime.
Explanation: A. This is a direct application of modus ponens. D is incorrect because the premise directly links GDP to crime in this context.
Question 4
Q4. A teacher states: 'Students who score above 90% will get an A. Maria scored 88%.' What valid conclusion can be drawn?
- A) Maria will not get an A.
- B) Maria will get an A.
- C) The grading criteria are flawed.
- D) Maria may still get an A.
Answer: Maria may still get an A.
Explanation: D. The premise only defines A for scores >90%. Below that, outcomes are uncertain. A is incorrect because 88% doesn't guarantee not getting an A.
Question 5
Q5. If 'All metals conduct electricity' and 'Copper is a metal', what conclusion logically follows?
- A) Copper conducts electricity.
- B) Copper is a semiconductor.
- C) Not all metals conduct electricity.
- D) Copper is non-metallic.
Answer: Copper conducts electricity.
Explanation: A. This is a direct syllogism. B fails because it contradicts the premise that copper is a metal.
Question 6
Q6. A politician says: 'Supporting this bill means you support free speech. Opposing it means you oppose free speech.' What fallacy is present?
- A) False dilemma
- B) Straw man
- C) Ad hominem
- D) Circular reasoning
Answer: False dilemma
Explanation: A. It creates a false binary between support and opposition. B/D incorrectly frame the argument's structure.
Question 7
Q7. Given: 'If it rains, the ground gets wet. The ground is wet.' What conclusion is logically valid?
- A) It rained.
- B) It did not rain.
- C) The ground got wet from another source.
- D) Insufficient information to determine the cause.
Answer: Insufficient information to determine the cause.
Explanation: D. The wet ground could result from other causes. A is the fallacy of affirming the consequent.
Question 8
Q8. A study claims: '90% of participants improved after treatment. Therefore, the treatment works.' What flaw exists?
- A) Sample size too small
- B) Lack of control group
- C) Confirmation bias
- D) Anecdotal evidence
Answer: Lack of control group
Explanation: B. Without a control group, improvement could be due to placebo. A/D are plausible but not explicitly addressed in the premise.
Question 9
Q9. If 'No reptiles are mammals' and 'All snakes are reptiles', what conclusion is valid?
- A) No snakes are mammals.
- B) Some snakes are mammals.
- C) All mammals are snakes.
- D) Reptiles are a subset of mammals.
Answer: No snakes are mammals.
Explanation: A. This is a categorical syllogism. B/D contradict the premises; C reverses the relationships.
Question 10
Q10. A teacher says: 'All students who study pass. Ahmad passed.' What can be logically concluded?
- A) Ahmad studied.
- B) Ahmad did not study.
- C) Passing requires studying.
- D) Nothing can be concluded about Ahmad's studying.
Answer: Nothing can be concluded about Ahmad's studying.
Explanation: D. The premise allows multiple pathways to passing. A is the fallacy of affirming the consequent.
Question 11
Q11. Given: 'All mammals have lungs. Whales are mammals.' What conclusion follows?
- A) Whales have lungs.
- B) Whales have gills.
- C) Mammals have gills.
- D) Not all whales are mammals.
Answer: Whales have lungs.
Explanation: A. Direct syllogistic conclusion. B/C/D contradict given premises. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 12
Q12. A doctor argues: 'This patient has a fever. All fevers are caused by infections. Therefore, this patient has an infection.' What's the flaw?
- A) Overgeneralization
- B) False cause
- C) Circular reasoning
- D) Ambiguity
Answer: Overgeneralization
Explanation: A. Not all fevers are infectious (e.g., autoimmune). B is possible but A better describes the specific error.
Question 13
Q13. If 'A implies B' is true, which statement is also necessarily true?
- A) B implies A
- B) Not A implies not B
- C) Not B implies not A
- D) A and B are independent
Answer: Not B implies not A
Explanation: C. This is the contrapositive, logically equivalent to the original statement. A/B/D represent converses or inverses.
Question 14
Q14. Given: 'If a number is even, it is divisible by 2. 14 is divisible by 2.' What conclusion follows?
- A) 14 is even.
- B) 14 is odd.
- C) 14 is a prime number.
- D) 14 is irrational.
Answer: 14 is even.
Explanation: A. This is modus ponens. B/D contradict the premise; C is unrelated to divisibility.
Question 15
Q15. Which argument form is logically valid?
- A) If P then Q. Q is true. Therefore P.
- B) If P then Q. Not P. Therefore not Q.
- C) If P then Q. P is true. Therefore Q.
- D) If P then Q. Not Q. Therefore P.
Answer: If P then Q. P is true. Therefore Q.
Explanation: C. This is modus ponens. A/B/D represent fallacies (affirming consequent, denying antecedent, etc.).
Question 16
Q16. Given: 'No reptiles are mammals. All snakes are reptiles.' What valid conclusion follows?
- A) No snakes are mammals.
- B) Some snakes are mammals.
- C) All mammals are snakes.
- D) Reptiles include mammals.
Answer: No snakes are mammals.
Explanation: A. This follows the syllogistic structure. B/D contradict premises; C reverses categories.
Question 17
Q17. If 'All A are B' and 'All B are C', what can be concluded?
- A) All A are C.
- B) Some C are not A.
- C) No A are C.
- D) B and C are the same set.
Answer: All A are C.
Explanation: A. This is a valid transitive syllogism. B is possible but not necessary. C/D contradict the premises.
Question 18
Q18. If all mammals have hair and all humans are mammals, which conclusion is logically valid?
- A) All humans have hair.
- B) Some humans are not mammals.
- C) Hair is only found in mammals.
- D) Non-mammals have hair.
Answer: All humans have hair.
Explanation: Premises directly link humans to mammals and mammals to hair. Option C introduces irrelevant scope.
Question 19
Q19. A student argues: If it rains, the match is canceled. The match was not canceled. What follows?
- A) It did not rain.
- B) It rained but the match continued.
- C) The cancellation policy changed.
- D) The match was rescheduled.
Answer: It did not rain.
Explanation: This uses modus tollens (If P→Q, ¬Q→¬P). Option B violates logical structure by assuming exceptions.
Question 20
Q20. Which statement must be true if 'No reptiles are mammals' and 'All snakes are reptiles'?
- A) Some snakes are not mammals.
- B) All mammals are snakes.
- C) Reptiles and mammals overlap.
- D) Snakes are not reptiles.
Answer: Some snakes are not mammals.
Explanation: Transitive exclusion applies: Snakes⊂Reptiles⊄Mammals. Some snakes are not mammals is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.