All birds have feathers. Penguins are birds. Which statement is logically sound?

All feathered animals are penguins.

If it snows, the roads are closed. The roads are closed. What can be concluded?

Roads close only when it snows.

All squares are rectangles. All rectangles have four sides. What must be true?

Some squares are not rectangles.

AKU Entry Test Logical Reasoning Logical Problems Set 2

AKU Entry Test Logical Reasoning Logical Problems — Set 2

Question 1
Q1. All mammals have lungs. Whales are mammals. Which conclusion logically follows?
- A) All whales have lungs.
- B) Some whales have gills.
- C) No whales have lungs.
- D) All non-mammals lack lungs.
Answer: All whales have lungs.
Explanation: Syllogism: All A are B. All C are A. Therefore, All C are B. Option B introduces irrelevant gills.
Question 2
Q2. If a student studies, they pass the exam. Maria passed the exam. Which conclusion is valid?
- A) Maria studied.
- B) Maria might have cheated.
- C) Maria did not study.
- D) Passing requires studying.
Answer: Maria studied.
Explanation: Affirming the consequent is invalid. Maria could have passed via other means.
Question 3
Q3. All birds have feathers. Penguins are birds. Which statement is logically sound?
- A) Penguins have feathers.
- B) All feathered animals are penguins.
- C) No penguins have beaks.
- D) Only penguins have feathers.
Answer: Penguins have feathers.
Explanation: Direct syllogism applies. Penguins have feathers is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 4
Q4. If it snows, the roads are closed. The roads are closed. What can be concluded?
- A) It snowed.
- B) It did not snow.
- C) Roads close only when it snows.
- D) Roads are sometimes closed.
Answer: Roads are sometimes closed.
Explanation: Closing roads could have other causes. Affirming the consequent (A) is invalid.
Question 5
Q5. All squares are rectangles. All rectangles have four sides. What must be true?
- A) All squares have four sides.
- B) Some squares are not rectangles.
- C) No rectangles are squares.
- D) Rectangles have equal sides.
Answer: All squares have four sides.
Explanation: Transitive logic applies. All squares have four sides is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 6
Q6. Either X is true or Y is false. X is false. What must be true?
- A) Y is false.
- B) Y is true.
- C) X is true.
- D) X and Y are both false.
Answer: Y is false.
Explanation: Disjunctive syllogism: If ¬X, then Y must be false. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 7
Q7. No reptiles are mammals. Some snakes are reptiles. What follows?
- A) Some snakes are not mammals.
- B) All snakes are mammals.
- C) No snakes are reptiles.
- D) All mammals are snakes.
Answer: Some snakes are not mammals.
Explanation: Logical contrapositive applies. Some snakes are not mammals is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 8
Q8. If a plant is a cactus, it needs little water. The rose needs little water. Conclusion?
- A) The rose is a cactus.
- B) The rose is not a cactus.
- C) All roses are cacti.
- D) Cacti may have other traits.
Answer: Cacti may have other traits.
Explanation: Affirming the consequent invalid. Cacti could share traits with non-cacti. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 9
Q9. All doctors are professionals. Some professionals are teachers. What is valid?
- A) Some doctors are teachers.
- B) All doctors are teachers.
- C) No teachers are doctors.
- D) Most professionals are doctors.
Answer: Some doctors are teachers.
Explanation: Overlap between sets is possible. Some doctors are teachers is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 10
Q10. If a polygon is regular, all sides are equal. The hexagon has unequal sides. Conclusion?
- A) The hexagon is irregular.
- B) The hexagon is regular.
- C) All regular hexagons are equal.
- D) Irregular polygons have equal angles.
Answer: The hexagon is irregular.
Explanation: Contrapositive logic: ¬Q → ¬P. The hexagon is irregular is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 11
Q11. Some students are athletes. All athletes are disciplined. What must be true?
- A) Some students are disciplined.
- B) All students are disciplined.
- C) No athletes are students.
- D) Disciplined people are athletes.
Answer: Some students are disciplined.
Explanation: Transitive overlap applies. Some students are disciplined is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 12
Q12. If a number is even, it is divisible by 2. 14 is divisible by 2. Conclusion?
- A) 14 is even.
- B) 14 is odd.
- C) All even numbers are 14.
- D) Divisibility implies evenness.
Answer: 14 is even.
Explanation: Valid contrapositive logic. 14 is even is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 13
Q13. All metals conduct electricity. Gold is a metal. What is valid?
- A) Gold conducts electricity.
- B) Gold is non-metallic.
- C) Non-metals conduct electricity.
- D) Only gold conducts electricity.
Answer: Gold conducts electricity.
Explanation: Direct syllogism applies. Gold conducts electricity is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 14
Q14. If it is a weekday, the library is open. The library is closed. Conclusion?
- A) It is a weekend.
- B) It is a weekday.
- C) Libraries close on weekdays.
- D) Weekdays vary by region.
Answer: It is a weekend.
Explanation: Valid contrapositive. It is a weekend is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 15
Q15. All mammals have hearts. Whales have hearts. Valid conclusion?
- A) Whales are mammals.
- B) All hearted animals are whales.
- C) No whales are mammals.
- D) Hearts exist only in mammals.
Answer: Whales are mammals.
Explanation: Affirms transitive property. Whales are mammals is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 16
Q16. Either Ali or Usman is telling the truth. Ali is lying. What follows?
- A) Usman is truthful.
- B) Usman is lying.
- C) Both are lying.
- D) Truth is subjective.
Answer: Usman is truthful.
Explanation: Disjunctive syllogism applies. Usman is truthful is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 17
Q17. All prime numbers >2 are odd. 17 is prime. What can be concluded?
- A) 17 is odd.
- B) 17 is even.
- C) All odd numbers are prime.
- D) Some even numbers are prime.
Answer: 17 is odd.
Explanation: Direct deduction from premises. 17 is odd is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 18
Q18. If a solution is acidic, it has pH <7. The juice has pH 3. Conclusion?
- A) The juice is acidic.
- B) The juice is basic.
- C) All acidic solutions are juice.
- D) pH 3 is neutral.
Answer: The juice is acidic.
Explanation: Direct conditional application. The juice is acidic is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 19
Q19. No birds are reptiles. All parrots are birds. Valid conclusion?
- A) No parrots are reptiles.
- B) All reptiles are parrots.
- C) Some parrots are reptiles.
- D) Birds include reptiles.
Answer: No parrots are reptiles.
Explanation: Transitive exclusion applies. No parrots are reptiles is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.
Question 20
Q20. If it is sunny, we play cricket. We did not play cricket. Conclusion?
- A) It was not sunny.
- B) It was sunny.
- C) Cricket requires rain.
- D) Sunny days are rare.
Answer: It was not sunny.
Explanation: Valid contrapositive. It was not sunny is correct because it matches what the question requires. USAT, HAT and MDCAT analytical sections repeat this pattern.