Syllogism problems
- 1. Statements: All the bottles are boxes. All the boxes are bags. Some bags are trays.
Conclusions:
- Some bottles are trays.
- Some trays are boxes.
- All the bottles are bags.
- Some trays are bags.
Options- A. Only (3) and (4)
- B. Only (1) and (2)
- C. Only (2) and (3)
- D. Only (1) and (4) Discuss
Correct Answer: Only (3) and (4)
Explanation:
Only (3) and (4) follow.
- 2. Statements: Some cars are jeeps. All the boxes are jeeps. All the pens are cars.
Conclusions:
- Some cars are boxes.
- No pen is jeep.
- Some boxes are cars.
Options- A. None of three
- B. Only (1) and (2)
- C. Only (1) and (3)
- D. Only (2) and (3) Discuss
Correct Answer: None of three
Explanation:
- 3. Statement:
All pins are rods. Some rods are chains. All chains are hammers.
Conclusions:
I. Some pins are hammers.
II. Some hammers are rods
III. No pin is hammer.
Options- A. Only I follows
- B. Only II follows
- C. Only III follows
- D. Only either I or III & II follows Discuss
Correct Answer: Only either I or III & II follows
Explanation:
All pins are rods + Some rods are chains = A + I = No conclusion Hence I and II does not follow. However, the two a complementary I-E pair, Hence either I or III follows. Some rods are chains + All chains are Hammers = I + A + I = Some rods are hammers ? conversion ? Some hammers are rods (I). Hence III follows.
- 4. Statement:
Some books are papers. Some papers are desks. All desks are chairs.
Conclusions:
I. Some books are desks.
II. Some papers are chairs.
III. Some books are chairs.
Options- A. None follows
- B. Only I follows
- C. Only II follows
- D. Only III follows Discuss
Correct Answer: None follows
Explanation:
I-type statements can't be combined.
- 5. Statement:
Some pots are buckets. All buckets are tubs. All tubs are drums.
Conclusions:
I. Some drums are pots.
II. All tubs are buckets.
II Some drums are buckets.
Options- A. Only I and II follows
- B. Only I and III follows
- C. Only II and III follows
- D. All follows Discuss
Correct Answer: Only I and III follows
Explanation:
All buckets are tubs(A) ? conversion ? Some tubs are buckets (I) Hence II does not follow. All buckets are tubs + All tubs are drums A + A = A = All buckets are drums ? conversion ? Some drums are buckets + All buckets are drums = A + A + I + = Some drums are pots(I). Hence II follows.
- 6. Statement:
All pins are bags. All chalks are bags. All needles are bags.
Conclusions:
I. Some needles are pins.
II. Some chalks are needles.
III. No needle is pin.
Options- A. Only I follows
- B. Only III follows
- C. Only either I or III follows
- D. Only either I or III and II follows Discuss
Correct Answer: Only either I or III follows
Explanation:
All pins are bags (A) ? conversion ? Some bags are pins (I). All needles are bags + Some bags are pins = A + I = No conclusion Hence I and III do not follow by combination. However, they from an complementary E-I pair, either I or III follows. Again, All chalks are bags + conversion of all needles are bags = A + I = No conclusion Hence II do not follow.
- 7. Statement:
Some buses are trucks. Some trucks are boats. No boat is jeep.
Conclusions:
I. Some jeeps are buses.
II. Some boats are buses.
III. Some jeeps are trucks.
Options- A. None follows
- B. Only I follows
- C. Only II follows
- D. Only III follows Discuss
Correct Answer: None follows
Explanation:
Some buses are trucks + Some trucks are boats = I + I = No conclusion Hence II and consequently do not follow Some trucks are boats + No boat is jeep = I + E = O = Some trucks are not jeeps. Hence III does not follow.
- 8. Statement:
All flowers are trees. All trees are jungles. No jungle is hill.
Conclusions:
I. No flower is hill.
II. No tree is hill
III. Some jungles are flowers.
Options- A. None follows
- B. Only I and II follows
- C. Only I and III follows
- D. Only II and III follows Discuss
Correct Answer: Only II and III follows
Explanation:
All flowers are trees + All trees are jungles = A + A = A = All flowers are jungles ? conversion ? Some jungles are flowers Hence III follows. All trees are jungle + No jungle is hill = A + E = E = No tree is hill. Hence III follows. All flowers are trees + No tree is hill. Hence II follows. All flowers are trees + No tree is hill = A + E = E = No flower is hill. Hence I follows.
- 9. Statement:
All tables are sofas. All sofas are beds. All beds are mats.
Conclusions:
I. Some mats are sofas.
II. Some beds are tables.
III. Some mats are tables.
Options- A. None follows
- B. Only II follows
- C. Only I and III follows
- D. Only II and III follows Discuss
Correct Answer:
Explanation:
All sofas are beds + All beds are mats = A + A = A = All sofas are mats ? conversion ? Some mats are sofas (I). Hence I follows. All tables are sofas + All sofas are beds = A + A = A = All tables are beds ? conversion ? Some beds are tables(I). Hence II follows. All tables are beds + All beds are mats = A + A = A = All tables are mats ? conversion ? Some mats are tables (I). Hence III follows.
- 10. Statement:
Some desks are chairs. Some chairs. Some chairs are pens. Some pens. Some pens are drawers.
Conclusions:
I. Some drawers are desks.
II. Some drawers is chairs.
III. No drawer is chair.
Options- A. None follows
- B. Only II follows
- C. Only III follows
- D. Only either II or III follow Discuss
Correct Answer: Only either II or III follow
Explanation:
I-type statements can't be combined no conclusion follow by combined But II and III make a complementary I-E pair, Hence either I or III follows.
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