Syllogism problems
- 1. Statements:
All crows are birds.
All peacocks are crows.
Conclusions:
I. All peacocks are birds.
II. All birds are peacocks.
Options- A. Both conclusions I and II follow
- B. Neither conclusion I nor II follows
- C. Only conclusion I follows
- D. Only conclusion II follows Discuss
Correct Answer: Only conclusion I follows
Explanation:
Both the Premises are Universal Affirmative (A-type).
All peacocks are crows. ? All crows are birds.
A + A ? A-type of Conclusion "All peacocks are birds."
This is Conclusion I.
- 2. Statements:
I. All squares are rectangles.
II. All rectangles are polygons.
Conclusion:
Options- A. Square is not a polygon.
- B. Square is a polygon.
- C. Square is a rectangle and polygon.
- D. Square is not a rectangle. Discuss
Correct Answer: Square is a rectangle and polygon.
Explanation:
Both the Premises are Universal Affirmative (A?type).
All squares are rectangles. ? All rectangles are polygons.
A + A ? A?type of Conclusion "All squares are polygons."
Thus, square is rectangle (given) and square is polygon (derived).
- 3. Statements:
a. Mary said, "Ann and I both have cats."
b. Ann said, "I don't have a cat."
c. Mary always tells the truth, but Ann sometimes lies.
Conclusions:
I. Ann has a cat.
II. Mary has a cat.
III. Ann is lying.
Options- A. II only
- B. I and II only
- C. I, II and III
- D. I only Discuss
Correct Answer: I, II and III
Explanation:
Mary always tells the truth. Therefore, both Mary and Ann have cats. Clearly, Ann is lying. Thus, all the Conclusions I, II and III follow.
- 4. Statements:
1. All stenographers are lazy.
2. Some men are stenographers.
Conclusions:
I. All lazy people are men.
II. Some men are lazy.
Options- A. Only Conclusion I follows
- B. Only Conclusion II follows
- C. Both Conclusion I and Conclusion II follow
- D. Neither Conclusion I nor Conclusion II follows Discuss
Correct Answer: Only Conclusion II follows
Explanation:
First Premise is Universal Affirmative (A-type).
Second Premise is Particular Affirmative (I-type).
Some men are stenographers. ? All stenographers are lazy.
I + A ? I-type of Conclusion "Some men are lazy".
This is Conclusion II.
- 5. Statements:
Some pens are pencils.
Some pencils are erasers.
Some erasers are sharpeners.
Conclusions:
I. Some sharpeners are pens.
II. Some pencils are sharpeners.
III. Some erasers are pens.
Options- A. None follows
- B. Only II follows
- C. Only III follows
- D. All follow Discuss
Correct Answer: None follows
Explanation:
All the three Premises are particular (I?type). No Conclusion follows from the two particular premises.
- 6. Statements:
All boys are tall.
Rajiv is a boy.
Conclusions:
I. Rajiv is tall.
II. Rajiv is not tall.
Options- A. Only Conclusion I follows
- B. Only Conclusion II follows
- C. Both Conclusion I and Conclusion II follow
- D. Neither Conclusion I nor Conclusion II follows Discuss
Correct Answer: Only Conclusion I follows
Explanation:
Both the Premises are Universal Affirmative (A ? type).
Rajiv is a boy. ? All boys are tall.
A + A ? A-type of Conclusion "Rajiv is tall".
This is Conclusion I.
Venn diagrams:
- 7. Statements:
1. All elephants are men.
2. All men are socks.
Conclusions:
I. Some socks are elephants.
II. All elephants are socks.
Options- A. Only Conclusion I follows
- B. Only Conclusion II follows
- C. Both Conclusions I and II follow
- D. Neither Conclusion I nor II follows Discuss
Correct Answer: Both Conclusions I and II follow
Explanation:
Both the Premises are Universal Affirmative (A?type).
All elephants are men. ? All men are socks.
A + A ? A?type of Conclusion "All elephants are socks."
This is Conclusion II.
Conclusion I is the Converse of it.
- 8. Statement:
Some radios are telephones. All telephones are mirrors. All mirrors are desks.
Conclusions:
I. Some radios are desks.
II. Some radios are mirrors.
III. Some desks are telephones.
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:
Some radios are telephones + All telephones are mirrors = I + A = I = Some radios are mirrors Hence II follows Some radios are mirrors + All mirrors are desks = I + A = I = Some radios are desks Hence I follows. All telephones are mirrors + All mirrors are desks = A + A + = All telephones are desks ? conversion ? Some desks are telephones (I). Hence III follows.
- 9. Statement:
All furniture are jungles. No jungle is road. Some road are hills.
Conclusions:
I. Some roads are furniture.
II. Some jungles are furniture.
III. Some hills are jungles.
Options- A. Only I follow
- B. Only II follow
- C. Only III follow
- D. Only I and III follow Discuss
Correct Answer: Only II follow
Explanation:
All furniture are jungles + No jungle is road = A + E = E = No furniture is road ? conversion ? No road is furniture (E) Hence I does not follows. All furniture are jungles (A) ? conversion ? Some jungles are furniture (I). Hence II follows. No jungle is road + Some roads are hills = E + I = O* = Some hills are not jungles Hence III does not follows.
- 10. Statement:
All brick are stones. Some stones are rocks. All rocks are mountains.
Conclusions:
I. Some mountains are stones.
II. Some mountains are bricks.
III. Some stones are bricks.
Options- A. Only I follow
- B. Only III follow
- C. Only I and III follow
- D. All follow Discuss
Correct Answer: Only I and III follow
Explanation:
Some stones are rocks + All rocks are mountains = I + A = I = Some stones are mountains ? conversion ? Some mountains are stones (I). Hence II follows. All brick are stones + Some stones are mountains = A + I = No conclusion Hence II does not follow. All brick are stones (A) ? conversion ? Some stone are bricks(I). Hence III follows.
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