Syllogism problems
- 1. Statement:
All flowers are trees. Some trees are houses All houses are wheels.
Conclusions:
I. Some wheels are trees.
II. Some trees are flowers.
III.Some wheels are flowers.
Options- A. Only I and II follow
- B. Only I and III follow
- C. Only II and III follow
- D. All I, II and III follow Discuss
Correct Answer: Only I and II follow
Explanation:
Some trees are houses + All houses are wheels = I + A = I = Some trees are wheels ? (I) conversion ? Some wheels are trees (I). Hence I follows. All flowers are tree ? (A) conversion ? Some trees are flowers (I). Hence II follows. But II and III can't, be combined as they are I -type statements Hence III does not follow.
- 2. Statement:
All windows are doors. All buildings are doors. All doors are boats.
Conclusions:
I. All windows are boats.
II. All buildings are boats.
III. Some boats are doors.
Options- A. Only I and II follow
- B. Only I and III follow
- C. Only II and III follow
- D. All follow Discuss
Correct Answer: All follow
Explanation:
All windows are doors + All doors are boats = A + A = A = All windows are boats. Hence I follows. All buildings are doors + All doors are boats = A + A = A = All buildings are boats. Hence II follows. All doors are boats (A) ? conversion ? Some boats are doors(I). Hence III follows.
- 3. Statement:
All buildings are mirrors. Some mirrors are pens. No pen is paper.
Conclusions:
I. Some papers are buildings.
II. Some pens are buildings.
III. Some papers are mirrors.
Options- A. None follow
- B. Only I follow
- C. Only II follow
- D. Only III follow Discuss
Correct Answer: None follow
Explanation:
Some mirrors are pens + No pen is paper = 1 + E = O* = Some mirrors are not papers Hence III does not follow. All buildings are mirrors + Some mirrors are pens = A + I = No conclusion Hence II and consequently I do not follow.
- 4. Statement:
Some books are trees. All tress are roads. All roads are wheels.
Conclusions:
I. Some wheels are books.
II. Some roads are books.
III. Some wheels are trees.
Options- A. Only I and II follow
- B. Only II & III follow
- C. Only I and III follow
- D. All follow Discuss
Correct Answer: All follow
Explanation:
Some books are trees + All tress are roads = I + A = I = Some books are roads (I) Hence II follows. Some books are trees + All roads are wheels = I + A = I = Some books are wheels ? conversion ? Some wheels are books (I) Hence I follows. All trees are roads + All roads are wheels = A + A = A = All trees are wheels ? conversion ? Some wheels are trees (I) Hence III follows.
- 5. Statement:
All stones are rivers. All rivers are cars. Some cars are trains.
Conclusions:
I. Some trains are stones.
II. Some cars are stones.
III. Some trains are rivers.
Options- A. None follows
- B. Only I follows
- C. Only II follows
- D. Only III follows Discuss
Correct Answer: Only II follows
Explanation:
All stones are rivers + All rivers are cars = A + A = A = All stones are cars ? conversion ? Some cars are stones (I) Hence II follows. All rivers are cars + Some cars are trains = I + A = No conclusion Hence II and consequently I do not follow.
- 6. Statement:
Some rivers are hills. No hill is taxi. All taxis are buses.
Conclusions:
I. Some buses are rivers.
II. Some taxis are rivers.
III. No bus is river.
Options- A. None follows
- B. Only I follows
- C. Only III follows
- D. Only II follows Discuss
Correct Answer:
Explanation:
Some rivers are hills + No hill is taxi = I + E = O = Some rivers are not taxis Hence II does not follow. Again, Since O-type statements can't be combined, neither I nor III follows. But the two form a complementary E- I pair, Hence either I or III follows.
- 7. In the following question a statement is followed by four inferences. Select the one which is most appropriate.
All the books, written by Prabhakar, are textbooks.
Some of his books are published by Pitamber Publishing Company.
Options- A. All the books published by Pitamber Publishing Company have been written by Prabhakar.
- B. Pitamber Publishing Company publishes some critical essays written by Prabhakar.
- C. Some textbooks written by Prabhakar are published by publishers other than Pitamber Publishing Company.
- D. Pitamber Publishing Company only publishes textbooks. Discuss
Correct Answer: Some textbooks written by Prabhakar are published by publishers other than Pitamber Publishing Company.
Explanation:
The given statement can be shown by the following diagram :
- 8. Statements:
I. Some keys are locks, some locks are numbers.
II. All numbers are letters, all letters are words.
Conclusions:
I. Some words are numbers.
II. Some locks are letters.
Options- A. Conclusion I follows
- B. Conclusion II follows
- C. Conclusions I and II follow
- D. None of the conclusion follows Discuss
Correct Answer: Conclusions I and II follow
Explanation:
Statement I consists of two Particular Affirmative (I-type) Premises.
Statement II consists of two Universal Affirmative (A-type) Premises.
Some locks are numbers. ? All numbers are letters.
I + A ? I-type of Conclusion "Some locks are letters".
This is Conclusion II.
All numbers are letters. ? All letters are words.
A + A ? A-type of Conclusion "All numbers are words".
Conclusion I is Converse of it.
- 9. Select the alternative inference which is most appropriate.
"All professors are learned; learned people are always gentle."
Inference: All professors are gentle persons.
Options- A. The inference is true.
- B. The inference is false.
- C. The inference is probably true or probably false.
- D. The inference is irrelevant. Discuss
Correct Answer: The inference is true.
Explanation:
All professors are learned and learned people are always gentle. So, all professors are gentle persons. It means the Inference is true.
- 10. For the Venn diagram given below, which of the following conclusion(s) is/are true?
I. Some Captains are painters.
II. Some Lieutenants are painters.
III. All Majors are soldiers.
IV. All Captains are soldiers.
V. All soldiers are painters.
Options- A. Only I and V follows
- B. Only I, III and IV follows
- C. Only II, IV and V follows
- D. Only III and IV follows Discuss
Correct Answer: Only III and IV follows
Explanation:
All Majors are captains.
All Majors are Lieutenants.
All Majors are Soldiers.
(This is Conclusion III )
All captains are Soldiers.
(This is Conclusion IV ).
All Lieutenants are Soldiers.
All Painters are Soldiers.
No Painter is Captain.
More in Verbal Reasoning:
Programming
Copyright ©CuriousTab. All rights reserved.