## 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:
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.

1. 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.

##### Correct Option: B

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.

1. 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.

1. 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.

##### Correct Option: C

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.

1. 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.

1. 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.

##### Correct Option: A

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.

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.