Syllogism problems
- 1. Statement:
Some bags are plates. Some plates are chairs. All chairs are tables.
Conclusions:
I. Some tables are plates.
II. Some chairs are bags.
III. No chair is bag.
Options- A. Only I follows
- B. Only either II or III follows
- C. Only I and either II or III follows
- D. Only III follows Discuss
Correct Answer: Only I and either II or III follows
Explanation:
Some pates are chairs + All chairs are tables = I + A = I = Some plates are tables ? conversion ? Some tables are plates(I). Hence I follows. Some bags are plates + Some plates are chairs = I + I = No conclusion Hence II and III do not follow. By combination. However, the two form a complementary E-I pair, Hence either I or III follows.
- 2. Statement:
All desks are rooms. Some rooms are halls. All halls are leaves.
Conclusions:
I. Some leaves are desks.
II. Some halls are desks.
III. Some leaves are rooms.
Options- A. None follows
- B. Only I follows
- C. Only II follows
- D. Only III follows Discuss
Correct Answer: Only III follows
Explanation:
Some rooms are halls + All halls are leaves = I + A = I = Some rooms are leaves ? conversion ? Some leaves are rooms(I) Hence III follows. All desks are rooms + Some rooms are halls = A + I = No conclusion Hence II and consequently I do not follow.
- 3. Statement:
Some doctors are lawyers. All teachers are lawyers. Some engineers are lawyers. All engineers are businessmen.
Conclusions:
I. Some teachers are doctors.
II. Some businessmen are lawyers.
III. Some businessmen are teachers.
IV. Some lawyers are teachers.
Options- A. None follows
- B. Only II follows
- C. Only III follows
- D. Only II and IV follow Discuss
Correct Answer: Only II and IV follow
Explanation:
All teachers are lawyers (A) ? conversion ? Some lawyers are teachers (I). Hence IV follows. Now, Some doctors are lawyers + Some lawyers are teachers = I + I = No conclusion Hence I does not follow. Some engineers are lawyers (I) ? conversion ? Some lawyers are engineers + All engineers are businessmen = I + A = I = Some lawyers are businessmen ? conversion Some businessmen are lawyers Hence II follows. But , All teachers are lawyers + Some lawyers are businessmen = A + I = No conclusion Hence III does not follow.
- 4. Statement:
All plastics are glasses.
Some sponges are glasses.
All sponges are clothes
All clothes are liquids.
Conclusions:
I. All liquids are sponges.
II. Some plastics are clothes.
III. All glasses are plastics.
IV. All liquids are clothes.
Options- A. None follows
- B. Only either II or IV follows
- C. Only IV follows
- D. Only II and IV follows Discuss
Correct Answer: None follows
Explanation:
All sponges are clothes + All clothes are liquids = A + A = All sponges are liquids ? conversion ? Some liquids are sponges (I). Hence I does not follows. All plastics are glasses + conversion of Some sponges are glasses = A + I = No conclusion Hence II does not follow. All plastics are glasses (A) ? conversion ? Some glasses are plastics (I) Hence III does not follow. All clothes are liquids(A) conversion Some liquids are clothes (I) Hence IV does not follow.
- 5. Statement:
All sands are beaches. All shores are beaches. Some beaches are trees. All trees are hotels.
Conclusions:
I. Some shores are hotels.
II. All beaches are shores
III. Some beaches are hotels.
IV. Some sands are trees.
Options- A. None follows
- B. Only II follows
- C. Only either I or III follows
- D. Only IV follows Discuss
Correct Answer:
Explanation:
Some beaches are tree + All trees are hotels = I + A = I = Some beaches are hotels Hence III follows. Now, All shores are beaches + Some beaches are hotels = A + I = No conclusion Hence I does not follow. All shores are beaches (A) ? conversion ? Some beaches are shores (I). Hence II does not follow. All sands are beaches + Some beaches are trees = A + I = No conclusion Hence IV does not follow.
- 6. Statement:
All parrots are pigeons. Some crows are pigeon. Some sparrows are crow. All sparrows are koels.
Conclusions:
I. Some koels are crows.
II. Some parrots are crows.
III. Some sparrows are pigeons.
IV. No crow is a parrot.
Options- A. None follows
- B. Only I follow
- C. Only II follows
- D. Only III follows Discuss
Correct Answer: Only II follows
Explanation:
Some sparrows are crow + Some crows are pigeons = I + I = No conclusion Hence III does not follow. Some crows are pigeons (I) ? conversion ? Some pigeons are crows (I) Now, all parrots are pigeons + Some pigeons are crows = A + I = No conclusion Hence II does not follow. Nor does IV follow. However conversion II from an I-E complementary pair with IV, Hence either I or IV follows. Some sparrows are crows(I) ? conversion ? Some crows are sparrows + All sparrows are koels ? conversion ? Some koels are crows (I). Hence I.
- 7. Statement:
All chairs are tables. All tables are cushions. Some cushions are trolleys. All trolleys are lamps.
Conclusions:
I. Some lamps are tables.
II. Some trolleys are chairs.
III. Some cushions are lamps.
IV. All chairs are cushions.
Options- A. Only I follows
- B. Only III and IV follow
- C. Only either II or II follows
- D. All follows Discuss
Correct Answer: Only III and IV follow
Explanation:
Some cushions are trolleys + All trolleys are lamps = I + A = I = Some cushions are lamps Hence III follows. All chairs are tables + All tables are cushions = A + A = A = All chairs are cushions Hence IV follows All tables are cushions + Some cushions are trolleys = A + I = No conclusion Hence I does not follow. All chairs are cushions + Some cushions are trolleys = A + I = No conclusion Hence II does not follow.
- 8. Statement:
Some roses are flowers. Some flowers are buds. All buds are leaves. All leaves are plants.
Conclusions:
I. Some plants are flowers.
II. Some roses are buds.
III. No leaves are roses.
IV. No roses are buds.
Options- A. Only I follows
- B. Only I & II follows
- C. Only I and either II or IV follows
- D. Only either II and IV follows Discuss
Correct Answer: Only I and either II or IV follows
Explanation:
Some flowers are buds + All buds are leaves + All leaves are plants = (I + A) + A = I = Some flowers are plants ? conversion ? Some plants are flowers (I). Hence I followers. Some roses are flowers + Some flowers are buds = I + I = No conclusion Hence II and IV do not follow by combination. Nor can III follow. However, II and IV form a complementary I-E pair, Hence either II or IV follows.
- 9. Statement:
Some grapes are apples. Some apples are bananas . All bananas are guavas.
No guava is pomegranates.
Conclusions:
I. No grapes are pomegranates.
II. Some guavas are grapes.
III. Some guavas are apples.
IV. No bananas are pomegranates.
Options- A. None follows
- B. Only I & III follows
- C. Either II or III follows
- D. Both III & IV follow Discuss
Correct Answer: Both III & IV follow
Explanation:
Some grapes are apples + Some apples are bananas = I + I = No conclusion So we can't move any further for ' grape' and this rules out I and II. Some apples are banana + All banana are guava = I + A = I = Some apples are guavas ? conversion ? Some guavas are apples (I). Hence III follows All bananas are guavas + No guava is pomegranates. Hence IV follows.
- 10. Statement:
Some doors are walls. All walls are floors. All floors are rooms. Some rooms are windows.
Conclusions:
I. All walls are rooms.
II. Some rooms are doors.
III. Some rooms are doors.
IV. Some floors are doors.
Options- A. None follows
- B. Only I & II follows
- C. Only II & III follows
- D. Only I, III & IV follows Discuss
Correct Answer: Only I, III & IV follows
Explanation:
All walls are floors + All floors are rooms = A + A = A = All walls are rooms Hence I follows. Some doors are walls + All walls are floors = I + A = I = Some doors are rooms ? conversion ? Some rooms are doors (I). Hence II follows. Conversion of gives us III. Some doors are walls + All walls are floors = I + A = I = Some doors (I) Hence IV follows.
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