## Syllogism

#### Syllogism

Direction: In each of the question below are Four statements following by Four conclusions numbered I, II, II and IV. You have to take the Four given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusion logically follows from the two statements disregarding commonly known fact.

1. 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.

1. 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.

##### Correct Option: C

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.

1. 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.

1. 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.

##### Correct Option: E

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.

1. 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.

1. 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.

##### Correct Option: A

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.

1. Statement:
Some doctors are lawyers. All teachers are lawyers. Some engineers are lawyers. All engineers are businessmen.
Conclusions:
I. Some teachers are doctors.
IV. Some lawyers are teachers.

1. 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.

##### Correct Option: D

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.

Direction: In each of the question below are three statements following by three conclusions numbered I, II and III. You have to take the three given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusion logically follows from the two statements disregarding commonly known fact.

1. 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.

1. 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.

##### Correct Option: D

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.