AMCAT Logical Reasoning: Deductive Logic 2 — Questions and Answers
Question 1: All roses are flowers. Some flowers are red. Which conclusion definitely follows?
- All roses are red
- Some roses are red
- No roses are red
- Some flowers are roses (Correct answer)
Correct answer: Some flowers are roses
From 'All roses are flowers', it follows by conversion that 'Some flowers are roses'.
'All roses are flowers' — by conversion of a universal affirmative, 'Some flowers are roses' is valid. There is no basis to conclude roses are red since 'some flowers are red' doesn't specify which flowers.
Question 2: No cats are dogs. All dogs are animals. Which is a valid conclusion?
- No cats are animals
- Some animals are not cats (Correct answer)
- All cats are animals
- Some dogs are cats
Correct answer: Some animals are not cats
All dogs are animals and no dog is a cat. So those dogs (which are animals) are not cats — some animals are not cats.
All dogs are animals (none of these dogs are cats, from premise 1). So among animals, there exist dogs who are definitely not cats. Therefore 'some animals are not cats' is valid.
Question 3: Statement: All pens are books. No book is a pencil. Conclusion I: No pen is a pencil. Conclusion II: Some books are pens.
- Only I follows
- Only II follows
- Both I and II follow (Correct answer)
- Neither follows
Correct answer: Both I and II follow
All pens are books and no book is a pencil → no pen is a pencil (I). All pens are books → some books are pens by conversion (II). Both follow.
Conclusion I: All pens are books; no book is pencil → no pen is pencil. Valid. Conclusion II: All pens are books → by conversion, some books are pens. Valid. Both follow.
Question 4: If no M is P, and all S is M, what can be concluded?
- No S is P (Correct answer)
- Some S is P
- All S is P
- Some M is P
Correct answer: No S is P
All S is M and no M is P. Since every S is an M, and no M is P, no S can be P.
All S ⊆ M, and M ∩ P = ∅. Therefore S ∩ P = ∅, meaning no S is P.
Question 5: Statements: Some teachers are writers. All writers are poets. Conclusion: Some teachers are poets.
- True (Correct answer)
- False
- Uncertain
- Partially true
Correct answer: True
Some teachers are writers. All writers are poets. Those teacher-writers are also poets → some teachers are poets. True.
Some teachers are writers (there is an overlap). All writers are poets (total inclusion). By syllogism, those overlapping teachers are also poets. Conclusion is definitely true.
Question 6: All A are B. All B are C. No C is D. Conclusion: No A is D.
- Definitely true (Correct answer)
- Definitely false
- Possibly true
- Cannot be determined
Correct answer: Definitely true
All A → B → C and no C is D. Since every A is a C, and no C is D, no A is D. Definitely true.
A ⊆ B ⊆ C and C ∩ D = ∅. Therefore A ∩ D = ∅ — no A is D. The conclusion is definitely true.
AMCAT Logical Reasoning: Deductive Logic 2
All roses are flowers.
Some flowers are red.
Which conclusion definitely follows?