## 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 stones are rivers. All rivers are cars. Some cars are trains.
Conclusions:
I. Some trains are stones.
II. Some cars are stones.
III. Some trains are rivers.

1. All stones are rivers + All rivers are cars = A + A = A = All stones are cars → conversion → Some cars are stones (I) Hence II follows. All rivers are cars + Some cars are trains = I + A = No conclusion Hence II and consequently I do not follow.

##### Correct Option: C

All stones are rivers + All rivers are cars = A + A = A = All stones are cars → conversion → Some cars are stones (I) Hence II follows. All rivers are cars + Some cars are trains = I + A = No conclusion Hence II and consequently I do not follow.

1. Statement:
Some rivers are hills. No hill is taxi. All taxis are buses.
Conclusions:
I. Some buses are rivers.
II. Some taxis are rivers.
III. No bus is river.

1. Some rivers are hills + No hill is taxi = I + E = O = Some rivers are not taxis Hence II does not follow. Again, Since O-type statements can't be combined, neither I nor III follows. But the two form a complementary E- I pair, Hence either I or III follows.

##### Correct Option: E

Some rivers are hills + No hill is taxi = I + E = O = Some rivers are not taxis Hence II does not follow. Again, Since O-type statements can't be combined, neither I nor III follows. But the two form a complementary E- I pair, Hence either I or III follows.

1. In the following question a statement is followed by four inferences. Select the one which is most appropriate.
All the books, written by Prabhakar, are textbooks.

1. Draw a figure and solve the question.

##### Correct Option: C

The given statement can be shown by the following diagram :

1. Statements:
I. Some keys are locks, some locks are numbers.
II. All numbers are letters, all letters are words.
Conclusions:
I. Some words are numbers.
II. Some locks are letters.

1. Statement I consists of two Particular Affirmative (I-type) Premises.
Statement II consists of two Universal Affirmative (A-type) Premises.
Some locks are numbers. ↔ All numbers are letters.

##### Correct Option: C

Statement I consists of two Particular Affirmative (I-type) Premises.
Statement II consists of two Universal Affirmative (A-type) Premises.
Some locks are numbers. ↔ All numbers are letters.
I + A ⇒ I-type of Conclusion “Some locks are letters”.
This is Conclusion II.
All numbers are letters. ↔ All letters are words.
A + A ⇒ A-type of Conclusion “All numbers are words”.
Conclusion I is Converse of it.

1. Statement:
All pins are rods. Some rods are chains. All chains are hammers.
Conclusions:
I. Some pins are hammers.
II. Some hammers are rods
III. No pin is hammer.

1. All pins are rods + Some rods are chains = A + I = No conclusion Hence I and III does not follow. However, the two a complementary I-E pair, Hence either I or III follows. Some rods are chains + All chains are Hammers = I + A + I = Some rods are hammers → conversion → Some hammers are rods (I). Hence II follows.

##### Correct Option: D

All pins are rods + Some rods are chains = A + I = No conclusion Hence I and II does not follow. However, the two a complementary I-E pair, Hence either I or III follows. Some rods are chains + All chains are Hammers = I + A + I = Some rods are hammers → conversion → Some hammers are rods (I). Hence III follows.