Syllogism problems
- 1. Statement:
Some birds are goats. Some goats are horses. Some horses are lions.
Some lions are tigers.
Conclusions:
I. Some tigers are goats.
II. No tiger is goat.
III. Some lions are birds.
IV. No lion is bird.
Options- A. Only either I or II follow
- B. Only either III or IV follows
- C. Only either I or II and either III or IV follow
- D. Only I and III follow Discuss
Correct Answer: Only either I or II and either III or IV follow
Explanation:
I- type statements can't be combined. However, II and II from a complementary I-E pair. So do III and IV Hence either I or II and either III or IV follows.
- 2. Statement:
All papers are bottles. All bottles are cups. Some cups are jugs.
Some jugs are plates.
Conclusions:
I. Some plates are cups.
II. Some plats are bottle.
III. Some cups are papers.
IV. Some bottles are papers.
Options- A. Only III and IV follow
- B. Only I and II follow
- C. Only I and III follow
- D. Only II and IV follow Discuss
Correct Answer: Only III and IV follow
Explanation:
Some cups are jugs + Some jugs are plates. = I + I = No conclusion Hence I does not follow. Nor does II follow All papers are bottles + All bottles are cups = A + A = A = All papers are cups ? conversion ? Some cups are papers(I) Hence III follows. All papers are bottles (A) ? conversion ? Some bottle are papers (I) Hence IV follows.
- 3. Statement:
All bulbs are wires. No wire is cable. Some cables are brushes. All brushes are paints.
Conclusions:
I. Some paints are cables.
II. Some wires are bulbs
III. Some brushes are wires.
IV. Some cables are bulbs.
Options- A. None follow
- B. Only I & II follows
- C. Only II follow
- D. Only III follow Discuss
Correct Answer: Only I & II follows
Explanation:
Some cables are brushes + All brushes are paints ? conversion ? Some paints are cables (I) Hence I follows. All bulbs are wires (A) ? conversion ? Some wires are bulbs (I) Hence II follows. No wire is cable + Some cables are brushes = I + E = O* = Some brushers are not wires Hence III does not follow. All bulbs is cable ? conversion ? No cable is bulb (E) Hence IV does not follow.
- 4. Statement:
All chairs are keys. All keys are balloons. Some balloons are mirrors.
Some mirrors are desks.
Conclusions:
I. Some desks are keys.
II. Some balloons are mirrors.
III. Some mirrors are balloons.
Options- A. Only I follow
- B. Only II follows
- C. Only III follow
- D. Only II and III follow Discuss
Correct Answer: Only II and III follow
Explanation:
All keys are balloons + Some balloons are mirrors = A + I = No conclusion Hence I does not follow. All chairs are keys + All keys are balloons = A + A = A = All chairs are balloons ? conversion ? Some balloons are chairs (I) Hence II follows. Some balloons are mirrors (I) ? conversion ? Some mirrors are balloons (I) Hence III follows.
- 5. Statement:
Some drums are posters.
All posters are windows.
Some windows are tablets.
All tablets are books.
Conclusions:
I. Some windows are drums.
II. Some books are posters.
III. Some tablets are drums.
Options- A. None follows
- B. Only I follows
- C. Only II follow
- D. Only III follow Discuss
Correct Answer: Only I follows
Explanation:
Some drums are posters + All posters are windows = I + A = I = Some drums are windows ? conversion ? Some windows are drums (I) Hence I follows. All posters are windows + Some windows are tablets = A + I = No conclusion Hence neither I or III follows.
- 6. Statement:
Some trains are cars. All cars are branches. All branches are nets.
Some nets are dresses.
Conclusions:
I. Some dresses are cars
II. Some nets are trains.
III. Some branches are trains
IV. Some dresses are trains.
Options- A. Only I and III follow
- B. Only II and III follow
- C. Only I and IV follow
- D. Only II, III and IV follow Discuss
Correct Answer: Only II and III follow
Explanation:
All branches are nets + Some nets are dresses = A + I = No conclusion Hence I and IV does not follow. Some trains are branches ? conversion ? Some branches are trains (I) Hence III follows. Some trains are branches + All branches are nets = I + A = I = Some trains are nets ? conversion ? Some nets are trains (I) Hence II follows.
- 7. Statement:
Some pencils are kites.
Some kites are desks.
All desks are jungles.
All jungles are mountains.
Conclusions:
I. Some mountains are pencils.
II. Some jungles are pencils.
III. Some mountains are desks
IV. Some jungles are kites.
Options- A. Only I and III follow
- B. Only I, II and III follow
- C. Only III and IV follow
- D. Only II, III and IV follow Discuss
Correct Answer: Only III and IV follow
Explanation:
Some kites are desks + All desks are jungles. = I + A = I = Some kites are jungles ? Conversion ? Some jungles are kites (I) Hence IV follows. some pencils are kites + Some jungles are kites = I + I = No conclusion Hence I and II does not follow. All desks are jungles + All jungles are mountains = A + A = A = All desks are mountains ? Conversion ? Some mountains are desks (I). Hence III follows.
- 8. Statement:
All papers are clips. Some chips are boards. Some boards are lanes.
All lanes are roads.
Conclusions:
I. Some roads are boards.
II. Some lanes are chips
III. Some boards are papers
IV. Some roads are chips.
Options- A. Only I and II follow
- B. Only I and III follow
- C. Only I, II and III follow
- D. Only II, III and IV follow Discuss
Correct Answer:
Explanation:
Some boards are lanes + All lanes are roads = I + A = I = Some boards are roads ? Conversion ? Some roads are boards (I). Hence I follows. Some chips are boards + Some boards are lanes = I + I = No conclusion Hence II and IV does not follow. All papers are clips + Some chips are boards = I + A = No conclusion Hence II and IV does not follow.
- 9. Statement:
All pens are clocks. Some clocks are tyres. Some tyres are wheels.
Some wheels are buses.
Conclusions:
I. Some buses are tyres.
II. Some wheels are clocks.
III. Some wheels are pens.
IV. Some buses are clocks.
Options- A. None follows
- B. Only I follows
- C. Only II follows
- D. Only III follows Discuss
Correct Answer: None follows
Explanation:
A + I and I + I both result is no conclusion.
- 10. Statement:
All stones are hammers. No hammer is a ring. Some rings are doors.
All doors are windows.
Conclusions:
I. Some windows are stones.
II. Some windows are rings.
III. No window is a stone.
IV. Some rings are stones.
Options- A. Only I follows
- B. Only II follows
- C. Only III follows
- D. Only either I or III follows Discuss
Correct Answer:
Explanation:
Some rings are doors + All doors are windows = I + A = I = Some rings are windows ? Conversion ? Some windows are rings(I) Hence II follows. All stones are hammers + No hammer is a ring = A + E = E No stones is a ring ? conversion ? No ring is a stone (E) Hence IV does not follows. No stone is a ring + Some rings are doors = E + I = O* = Some windows are not stones Hence either I or II follows as they form a complementary I-E pair.
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