Question 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.

Accepted Answer

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.

Question 2

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.

Accepted Answer

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.

Question 3

Statement: All buildings are mirrors. Some mirrors are pens. No pen is paper. Conclusions: I. Some papers are buildings. II. Some pens are buildings. III. Some papers are mirrors.

Accepted Answer

Some mirrors are pens + No pen is paper = 1 + E = O* = Some mirrors are not papers Hence III does not follow. All buildings are mirrors + Some mirrors are pens = A + I = No conclusion Hence II and consequently I do not follow.

Question 4

Statement: Some books are trees. All tress are roads. All roads are wheels. Conclusions: I. Some wheels are books. II. Some roads are books. III. Some wheels are trees.

Accepted Answer

Some books are trees + All tress are roads = I + A = I = Some books are roads (I) Hence II follows. Some books are trees + All roads are wheels = I + A = I = Some books are wheels → conversion → Some wheels are books (I) Hence I follows. All trees are roads + All roads are wheels = A + A = A = All trees are wheels → conversion → Some wheels are trees (I) Hence III follows.

Question 5

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.

Accepted Answer

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.

Question 6

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.

Accepted Answer

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.

Question 7

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. Some of his books are published by Pitamber Publishing Company.

Accepted Answer

The given statement can be shown by the following diagram :

Question 8

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.

Accepted Answer

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.

Question 9

Select the alternative inference which is most appropriate. "All professors are learned; learned people are always gentle." Inference: All professors are gentle persons.

Accepted Answer

All professors are learned and learned people are always gentle. So, all professors are gentle persons. It means the Inference is true.

Question 10

For the Venn diagram given below, which of the following conclusion(s) is/are true? I. Some Captains are painters. II. Some Lieutenants are painters. III. All Majors are soldiers. IV. All Captains are soldiers. V. All soldiers are painters.

Accepted Answer

All Majors are captains. All Majors are Lieutenants. All Majors are Soldiers. (This is Conclusion III ) All captains are Soldiers. (This is Conclusion IV ). All Lieutenants are Soldiers. All Painters are Soldiers. No Painter is Captain.

Question 11

Statements : Some peons are poor. X is poor. Conclusions : I. X is a peon. II. X has a large family.

Accepted Answer

The first premise is particular Affirmative (I- Type). The second premise is Universal Affirmative (A-Type). We can align the premises by converting the first premise and changing their order. Thus, X is poor → Some poors are peons have a doctorate degree. We know that, A + I = No conclusion.

Question 12

Statements: (A) All basketball players are tall men. (B). All basketball players are athletes. Conclusions: I. All tall men are basketball players. II. All athletes are basketball players.

Accepted Answer

Both the Premises are Universal Affirmative (A-type). We can align the Premises by taking converse of any of the premises. Some tall men are basketball players ↔ All basketball players are athletes. I + A ⇒I - type of conclusion "Some tall men are athletes".

Question 13

Statements: Some doctors are teachers. All teachers are counsellors. Conclusions: I. Some counsellors are not teachers. II. Some doctors are counsellors

Accepted Answer

First premise is Particular Affirmative (I–type). Second premise is Universal Affirmative (I-type). Both the premises are already aligned. Thus, Some doctors are teachers ↔ All teachers are counsellors. We know that, I + A ⇒ I-type conclusion. Therefor, our derived conclusion would be: "Some doctors are counsellors". Thus, only conclusion II follows.

Question 14

Statement: (a) All politicians are intelligent (b) Some women are politicians Conclusions: I. Some women are intelligent II. All those intelligent are women.

Accepted Answer

Some women are politicians. ↔ All politicians are intelligents. We know that, I + A ⇒I–type Conclusion Thus, our derived Conclusion would be: "Some women are intelligent".

Question 15

Statements: (A) Some cats are dogs. (B) Some dogs are stones. Conclusions: I. No cat is stone. II. All dogs are stones. III. Some stones are cats. IV. No dog is cat.

Accepted Answer

Both the Premises are Particular Affirmative (I-type). No Conclusion follows from the two Particular Premises. Conclusions I and III form Complementary Pair. Therefore, either Conclusion I or III follows. Considering the given Options we can select option (4) as the answer.

Question 16

Statements: A. All girls are proud. B. All proud will be humiliated one day. Inferences: I. All girls will be humiliated one day. II. Some girls will be humiliated one day.

Accepted Answer

Both the Premises are Universal Affirmative (A-type). Both the Premises are already aligned. All girls are proud ↔ All proud will be humiliated one day We know that, A + A ⇒ A – type Conclusion Therefore, our derived Conclusion would be: "All girls will be humiliated one day". Conclusion II is the converse of the derived Conclusion. Thus, both the Conclusions follow.

Question 17

Statements: P. All men are women. Q. All women are crazy. Conclusions: I. All men are crazy. II. All the crazy are men. III. Some of the crazy are men. IV. Some of the crazy are women.

Accepted Answer

Both the Premises are Universal Affirmative (A-type). All men are women. ↔ All women are crazy. A + A ⇒ A – type of Conclusion "All men are crazy". This is Conclusion I. Conclusion III is the Converse of it. Conclusion IV is the Converse of Statement Q.

Question 18

Statements: All Americans are English speaking. No Eskimos are English speaking. Conclusions: I. No Eskimos are Americans. II. No English-speakers are Eskimos.

Accepted Answer

We can align the premises by converting the second premise. All Americans are English speaking. ↔ No English speakers are Eskimos. We know that, A + E → E type conclusion Thus, our derived conclusion would be: "No Americans are Eskimos." Conclusion I is the converse of the derived conclusion. Conclusion II is the converse of second premise.

Question 19

Statements: (a) All frogs are tortoises. (b) No tortoise is a crocodile. Conclusions: I. No crocodile is a frog. II. No frog is a crocodile.

Accepted Answer

First Premise is Universal Affirmative (A-type). Second Premise is Universal Negative (E-type). All frogs are tortoises. ↔ No tortoise is a crocodile. A + E ⇒ E-type of Conclusion "No frog is a crocodile". This is Conclusion II. Conclusion I is Converse of this Conclusion.

Question 20

Statements: (a) All dogs are books (b) All books are pictures. Conclusion: I. All dogs are pictures. II. All books are dogs. III. All pictures are dogs. IV. Some pictures are books.

Accepted Answer

Both the Premises are Universal Affirmative (A-type). All dogs are books. ↔ All books are pictures. A + A ⇒ A-type of Conclusion "All dogs are pictures." This is Conclusion I. Conclusion IV is Converse of the second Premise.

Syllogism Questions