Crossover Aptitude Test Logical Reasoning: Syllogisms 3 — Questions and Answers
Question 1: Statement 1: All cars are vehicles. Statement 2: All vehicles need fuel. Conclusion: All cars need fuel. Is the conclusion:
- False
- True (Correct answer)
- Uncertain
- Partially true
Correct answer: True
Both premises are universal affirmatives, so the conclusion that all cars need fuel necessarily follows.
Question 2: Some athletes are vegetarians. All vegetarians avoid meat. Which is definitely true?
- All athletes avoid meat.
- No athletes avoid meat.
- Some athletes avoid meat. (Correct answer)
- Vegetarians are not athletes.
Correct answer: Some athletes avoid meat.
The athletes who are vegetarians must avoid meat, so some athletes avoid meat.
Question 3: No mammals are cold-blooded. All fish are cold-blooded. Therefore:
- Some fish are mammals.
- No fish are mammals. (Correct answer)
- All mammals are fish.
- Some mammals are cold-blooded.
Correct answer: No fish are mammals.
Mammals cannot be cold-blooded, and fish must be cold-blooded, so the two groups cannot overlap.
Question 4: All P are Q. Some Q are R. Which conclusion is INVALID?
- Some Q are P.
- All P are Q.
- All P are R. (Correct answer)
- Some R may be P.
Correct answer: All P are R.
We cannot conclude all P are R because only some Q (which contains P) are R.
Question 5: All honest people keep promises. John does not keep promises. Therefore:
- John is honest.
- John is not honest. (Correct answer)
- Some honest people are like John.
- John sometimes keeps promises.
Correct answer: John is not honest.
By contrapositive, if someone doesn't keep promises, they are not honest.
Question 6: Some books are fiction. All fiction entertains. Some books are textbooks. What can be concluded?
- All books entertain.
- Some books entertain. (Correct answer)
- Textbooks are fiction.
- No books are textbooks.
Correct answer: Some books entertain.
The books that are fiction entertain, so at least some books entertain.
Question 7: All M are N. All N are O. No O are P. Therefore:
- All M are P.
- Some M are P.
- No M are P. (Correct answer)
- Some N are P.
Correct answer: No M are P.
M is entirely within N, N is entirely within O, and O has no overlap with P, so M has no overlap with P.
Crossover Aptitude Test Logical Reasoning: Syllogisms 3
Statement 1: All cars are vehicles.
Statement 2: All vehicles need fuel.
Conclusion: All cars need fuel.
Is the conclusion: