AMCAT Logical Reasoning: Syllogisms 2 — Questions and Answers
Question 1: All birds can fly. A penguin is a bird. Conclusion: A penguin can fly. This argument is:
- Valid and sound
- Invalid logically
- Valid but unsound (Correct answer)
- Invalid — logical error
Correct answer: Valid but unsound
The argument is logically valid (conclusion follows from premises) but unsound because 'All birds can fly' is factually false.
A syllogism is VALID if the conclusion necessarily follows from premises. It is SOUND if valid AND all premises are true. The form is valid, but 'All birds can fly' is false, making it valid but unsound.
Question 2: Some students are athletes. All athletes are disciplined. Conclusion: Some students are disciplined.
- True (Correct answer)
- False
- Cannot be determined
- Only if all students are athletes
Correct answer: True
Those students who are athletes are also disciplined → some students are disciplined. True.
Let X = student-athletes (non-empty). X is a subset of athletes. All athletes are disciplined, so X is also disciplined. Therefore some students are disciplined.
Question 3: No reptile is a mammal. A whale is a mammal. Conclusion: A whale is not a reptile.
- True (Correct answer)
- False
- Uncertain
- Partially true
Correct answer: True
'No reptile is a mammal' is equivalent to 'No mammal is a reptile'. A whale is a mammal → A whale is not a reptile.
'No reptile is a mammal' (E-type proposition) is symmetric: 'No mammal is a reptile'. Since a whale is a mammal, it follows that a whale is not a reptile.
Question 4: All M are N. Some N are O. Can we conclude 'Some M are O'?
- Yes
- No (Correct answer)
- Only if all N are O
- Only if some M are N
Correct answer: No
The N's that are O may be entirely different from the N's that are M. We cannot conclude 'Some M are O'.
All M is a subset of N. Some N overlap with O. But the N's in O could be entirely outside the M subset of N. Without knowing the overlap includes M, we cannot conclude some M are O.
Question 5: Some A are B. Some B are C. Conclusion: Some A are C.
- Definitely true
- Definitely false
- May or may not be true (Correct answer)
- True only if all B are C
Correct answer: May or may not be true
The A-B overlap and B-C overlap may be completely disjoint sets of B. No definite conclusion.
Example: A={1,2}, B={2,3,4}, C={3,5}. Some A are B (2 is in both), some B are C (3 is in both), but no A are C. So the conclusion does not definitely follow.
Question 6: All dogs are animals. All animals are living beings. No living being is a machine. Conclusion: No dog is a machine.
- True (Correct answer)
- False
- Uncertain
- Partially true
Correct answer: True
Dogs are subset of animals, which are subset of living beings. No living being is a machine, so no dog is a machine.
Dog subset of animal subset of living being. Living being and machine are disjoint. Therefore dog and machine are disjoint — no dog is a machine. True.
AMCAT Logical Reasoning: Syllogisms 2
All birds can fly.
A penguin is a bird.
Conclusion: A penguin can fly.
This argument is: