## Syllogism

#### Syllogism

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 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.

1. 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.

##### Correct Option: D

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.

1. 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.

1. 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.

##### Correct Option: E

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.

1. 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.

1. 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.

##### Correct Option: D

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.

1. Statement:
All flowers are trees. Some trees are houses All houses are wheels.
Conclusions:
I. Some wheels are trees.
II. Some trees are flowers.
III.Some wheels are flowers.

1. Some trees are houses + All houses are wheels = I + A = I = Some trees are wheels → (I) conversion → Some wheels are trees (I). Hence I follows. All flowers are tree → (A) conversion → Some trees are flowers (I). Hence II follows. But II and III can't, be combined as they are I -type statements Hence III does not follow.

##### Correct Option: A

Some trees are houses + All houses are wheels = I + A = I = Some trees are wheels → (I) conversion → Some wheels are trees (I). Hence I follows. All flowers are tree → (A) conversion → Some trees are flowers (I). Hence II follows. But II and III can't, be combined as they are I -type statements Hence III does not follow.

1. Statement:
All windows are doors. All buildings are doors. All doors are boats.
Conclusions:
I. All windows are boats.
II. All buildings are boats.
III. Some boats are doors.

1. All windows are doors + All doors are boats = A + A = A = All windows are boats. Hence I follows. All buildings are doors + All doors are boats = A + A = A = All buildings are boats. Hence II follows. All doors are boats (A) → conversion → Some boats are doors(I). Hence III follows.

##### Correct Option: D

All windows are doors + All doors are boats = A + A = A = All windows are boats. Hence I follows. All buildings are doors + All doors are boats = A + A = A = All buildings are boats. Hence II follows. All doors are boats (A) → conversion → Some boats are doors(I). Hence III follows.