# Three premise arguments based logical resoning for SSC Exams

Dec 5, 2016 16:55 IST

In this article, we have displayed a set of 25 questions based on the Three premise Arguments. This is made for the sake of sharpening your reasoning skills. As Students appearing in SSC CGL or CHSL face the difficulty in this chapter.

In two premise arguments, there are three statements and several conclusions are given, i.e. 2-5 in numbers and you have to find out which conclusion is satisfying/ meeting the meaning of statements. This type of logical reasoning is the simplest among all others.

In Logic, every categorical statement is termed as “Proposition”. The standard proposition is comprised of Quantifier, Subject, Copula and Predicate.

After identifying this, Statements are identified on the ground of Quantity, Quality and Distribution. After that conclusion is decided by using the following concepts.

a.       Immediate Deductive Inference

b.      Mediate Deductive Inference

Important Points to Remember: -

During deriving the logical conclusions, remember the following points.

i.                     The converse of the conclusions derived.

ii.                   The Converse of each of the given premises.

iii.                  The conclusion that follows from the given premises directly in accordance with the rules of syllogism.

Type 2: Three-Premise Arguments

Directions: (Question 1 to 19) In each of the questions below are given three statements followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance with the commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

1. Statements: All dolls are windows. All bottles are windows. All cars are bottles.

Conclusions: I. All cars are windows.

II. Some cars are dolls.

III. Some windows are cars.

a. Only I and II follow

b. Only II and III follow

c. Only I and III follow

d. All follow

e. None of these

2. Statements: All fruits are vegetables. All pens are vegetables. All vegetables are rains.

Conclusions: I. All fruits are rains.

II. All pens are rains.

III. Some rains are vegetables.

a. None follows

b. Only I and II follow

c. Only II and III follow

d. Only I and III follow

e. All follow

3. Statements: All snakes are trees. Some trees are roads. All roads are mountains.

Conclusions: I. Some mountains are snakes.

II. Some roads are snakes.

III. Some mountains are trees.

a. Only I follows

b. Only II follows

c. Only III follows

d. Both I and II follow

e. None follows

4. Statements: Some hills are rivers. Some rivers are deserts. All deserts are roads.

Conclusions: I. Some roads are rivers.

II. Some roads are hills.

III. Some deserts are hills.

a. None follows

b. Only I follows

c. Only I and II follow

d. Only II and III follow

e. All follow

5. Statements: Some blades are hammers. Some hammers are knives. Some knives are axes.

Conclusions: I. Some axes are hammers.

II. Some knives are blades.

III. Some axes are blades.

a. None follows

b. Only I follows

c. Only II follows

d. Only III follows

e. None of these

6. Statements: All trees are flowers. No flower is fruit. All branches are fruits.

Conclusions: I. Some branches are trees.

II. No fruit is tree.

III. No tree is branch.

a. None follows

b. Only either I or III follows

c. only II follows

d. Only either I or III, and II follow

e. None of these

7. Statements: All tigers are lions. No cow is lion. Some camels are cows.

Conclusions: I. Some lions are camels.

II. No camel is tiger.

III. Some tigers are cows.

a. None follows

b. Only I follows

c. Only II follows

d. Only III follows

e. Either I or II follows

8. Statements: Some towels are brushes. No brush is soap. All soaps are rats.

Conclusions: I. Some rats are brushes.

II. No rate is brush.

III. Some towels are soaps.

a. None follows

b. Only either I or II follows

c. Only II follows

d. Only I and III follow

e. None of these

9. Statements: Some pens are books. All schools are books. Some colleges are schools.

Conclusions: I. Some colleges are pens.

II. Some pens are schools.

III. Some colleges are books.

a. Only I and II follow

b. Only II and III follow

c. Only I and III follow

d. All follow

e. None of these

10. Statements: All tigers are jungles. No jungle is bird. Some birds are rains.

Conclusions: I. No rains is jungle.

II. Some rains are jungles.

III. No bird is tiger.

a. Only I and II follow

b. Only III follows

c. Only either I or II, and III follow

d. All follow

e. None of these

11. Statements: All flowers are toys. Some toys are trees. Some angels are trees.

Conclusions: I. Some angels are toys.

II. Some trees are flowers.

III. Some flowers are angles.

a. None follows

b. Only I follows

c. Only II follows

d. Only III follows

e. Only I and III follow

12. Statements: All trains are buses. No room is bus. All boats are rooms.

Conclusions: I. No boat is train.

II. No bus is boat.

III. No train is room.

a. None follows

b. Only I and II follow

c. Only II and III follow

d. Only I and III follow

e. All follow

13. Statements: No rabbit is lion. Some horses are lions. All rabbits are tables.

Conclusions: I. Some tables are lions.

II. Some horses are rabbits.

III. No lion is table.

a. None follows

b. Only either I or III follows

c. Only II and III follow

d. Only III follows

e. None of these

14. Statements: Some mountains are hillocks. Some mountains are rivers. Some mountains are valleys.

Conclusions: I. All mountains are either hillocks or rivers or valleys.

II. No valley is river.

III. Some river are valleys.

a. None follows

b. Only I follows

c. Only either II or III follows

d. Only III follows

e. None of these

15. Statements: Some boxes are hammers. Some hammers are beads. All beads are rings.

Conclusions: I. Some rings are hammers.

II. Some hammers are boxes.

III. Some rings are boxes.

a. None follows

b. Only I follows

c. Only I and II follow

d. Only II and III follow

e. All follow

16. Statements: Some blankets are the beds. Some pillows are blankets. All beds are pillows.

Conclusions: I. Some blankets are pillows.

II. Some pillows are the beds.

III. Some beds are blankets

a. Only either I or II follows

b. Only I and either II or III follow

c. Only III and either I or II follow

d. All I, II and III follow

e. None of these

17. Statements: Some pictures are frames. Some frames are idols. All idols are curtains.

Conclusions: I. Some curtains are pictures.

II. Some curtains are frames.

III. Some idols are frames.

a. Only I and II follow

b. Only II and III follow

c. Only I and III follow

d. All follow

e. None of these

18. Statements: Some rats are cats. Some cats are dogs. No dog is cow.

Conclusions: I. No cow is cat.

II. No dog is rat.

III. Some cats are rats.

a. None follows

b. Only I and II follow

c. Only II and III follow

d. Only III follows

e. All I, II and III follow

19. Statements: Some uniforms are covers. All covers are papers. All papers are bags.

Conclusions: I. All covers are bags.

II. Some bags are covers, papers and uniforms.

III. Some uniforms are not papers.

a. Only I follows

b. Only I and II follow

c. Only III follows

d. All I, II and III follow

e. None of these

Directions (Questions 20 to 25): In each of the following questions, three statements are given followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

20. Statements: All pencils are birds. All birds are skies. All skies are hills.

Conclusions: I. All pencils are hills.

II. All hills are birds

III. All skies are pencils.

IV. All birds are hills.

a. Only I and II follow

b. Only I and III follow

c. Only III and IV follow

d. All follow

e. None of these

21. Statements: All needles are threads. All threads are boxes. All trees are boxes.

Conclusions: I. No needle is tree.

II. Some trees are threads.

III. Some boxes are needles.

IV. Some trees are needles.

a. None follows

b. Only either I or IV follows

c. Only either I or IV, and II follow

d. Only III follows

e. Only either I or IV, and III follow

22. Statements: All jungles are buses. All books are buses. All fruits are books.

Conclusions: I. Some fruits are jungles.

II. Some buses are books.

III. Some buses are jungles.

IV. All fruits are buses.

a. Only I, II and III follow

b. Only I, II and IV follow

c. Only II, III and IV follow

d. All follow

e. None of these

23. Statements: Some spoons are bowls. All bowls are knives. All knives are forks.

Conclusions: I. All spoons are forks.

II. All bowls are forks.

III. Some knives are bowls.

IV. Some forks are spoons.

a. Only II and III follow

b. Only II and IV follow

c. Only III and IV follow

d. All follow

e. None of these

24. Statements: All players are spectators. Some spectators are theatres. Some theatres are dramas.

Conclusions: I. Some dramas are spectators.

II. Some players are dramas.

III. Some theatres are players.

IV. All spectators are players.

a. None follows

b. Only I and III follow

c. Only II follows

d. Only II and IV follow

e. All follow

25. Statements: All benches are desks. Some desks are roads. All road are pillars.

Conclusions: I. Some pillars are benches.

II. Some pillars are desks.

III. Some roads are benches.

IV. No pillar is a bench.

a. None follows

b. Only either I or IV, and III follow

c. Only either I or IV follows

d. Only either I or IV, and II follow

e. All follow

Complete Answer key

All the Best!!!!

After identifying this, Statements are identified on the ground of Quantity, Quality and Distribution. After that conclusion is decided by using the following concepts.

a.       Immediate Deductive Inference

b.      Mediate Deductive Inference

Important Points to Remember: -

During deriving the logical conclusions, remember the following points.

i.                     The converse of the conclusions derived.

ii.                   The Converse of each of the given premises.

iii.                  The conclusion that follows from the given premises directly in accordance with the rules of syllogism.

Type 2: Three-Premise Arguments

Directions: (Question 1 to 19) In each of the questions below are given three statements followed by three conclusions numbered I, II and III. You have to take the given statements to be true even if they seem to be at variance with the commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

1. Statements: All dolls are windows. All bottles are windows. All cars are bottles.

Conclusions: I. All cars are windows.

II. Some cars are dolls.

III. Some windows are cars.

a. Only I and II follow

b. Only II and III follow

c. Only I and III follow

d. All follow

e. None of these

2. Statements: All fruits are vegetables. All pens are vegetables. All vegetables are rains.

Conclusions: I. All fruits are rains.

II. All pens are rains.

III. Some rains are vegetables.

a. None follows

b. Only I and II follow

c. Only II and III follow

d. Only I and III follow

e. All follow

3. Statements: All snakes are trees. Some trees are roads. All roads are mountains.

Conclusions: I. Some mountains are snakes.

II. Some roads are snakes.

III. Some mountains are trees.

a. Only I follows

b. Only II follows

c. Only III follows

d. Both I and II follow

e. None follows

4. Statements: Some hills are rivers. Some rivers are deserts. All deserts are roads.

Conclusions: I. Some roads are rivers.

II. Some roads are hills.

III. Some deserts are hills.

a. None follows

b. Only I follows

c. Only I and II follow

d. Only II and III follow

e. All follow

5. Statements: Some blades are hammers. Some hammers are knives. Some knives are axes.

Conclusions: I. Some axes are hammers.

II. Some knives are blades.

III. Some axes are blades.

a. None follows

b. Only I follows

c. Only II follows

d. Only III follows

e. None of these

6. Statements: All trees are flowers. No flower is fruit. All branches are fruits.

Conclusions: I. Some branches are trees.

II. No fruit is tree.

III. No tree is branch.

a. None follows

b. Only either I or III follows

c. only II follows

d. Only either I or III, and II follow

e. None of these

7. Statements: All tigers are lions. No cow is lion. Some camels are cows.

Conclusions: I. Some lions are camels.

II. No camel is tiger.

III. Some tigers are cows.

a. None follows

b. Only I follows

c. Only II follows

d. Only III follows

e. Either I or II follows

8. Statements: Some towels are brushes. No brush is soap. All soaps are rats.

Conclusions: I. Some rats are brushes.

II. No rate is brush.

III. Some towels are soaps.

a. None follows

b. Only either I or II follows

c. Only II follows

d. Only I and III follow

e. None of these

9. Statements: Some pens are books. All schools are books. Some colleges are schools.

Conclusions: I. Some colleges are pens.

II. Some pens are schools.

III. Some colleges are books.

a. Only I and II follow

b. Only II and III follow

c. Only I and III follow

d. All follow

e. None of these

10. Statements: All tigers are jungles. No jungle is bird. Some birds are rains.

Conclusions: I. No rains is jungle.

II. Some rains are jungles.

III. No bird is tiger.

a. Only I and II follow

b. Only III follows

c. Only either I or II, and III follow

d. All follow

e. None of these

11. Statements: All flowers are toys. Some toys are trees. Some angels are trees.

Conclusions: I. Some angels are toys.

II. Some trees are flowers.

III. Some flowers are angles.

a. None follows

b. Only I follows

c. Only II follows

d. Only III follows

e. Only I and III follow

12. Statements: All trains are buses. No room is bus. All boats are rooms.

Conclusions: I. No boat is train.

II. No bus is boat.

III. No train is room.

a. None follows

b. Only I and II follow

c. Only II and III follow

d. Only I and III follow

e. All follow

13. Statements: No rabbit is lion. Some horses are lions. All rabbits are tables.

Conclusions: I. Some tables are lions.

II. Some horses are rabbits.

III. No lion is table.

a. None follows

b. Only either I or III follows

c. Only II and III follow

d. Only III follows

e. None of these

14. Statements: Some mountains are hillocks. Some mountains are rivers. Some mountains are valleys.

Conclusions: I. All mountains are either hillocks or rivers or valleys.

II. No valley is river.

III. Some river are valleys.

a. None follows

b. Only I follows

c. Only either II or III follows

d. Only III follows

e. None of these

15. Statements: Some boxes are hammers. Some hammers are beads. All beads are rings.

Conclusions: I. Some rings are hammers.

II. Some hammers are boxes.

III. Some rings are boxes.

a. None follows

b. Only I follows

c. Only I and II follow

d. Only II and III follow

e. All follow

16. Statements: Some blankets are the beds. Some pillows are blankets. All beds are pillows.

Conclusions: I. Some blankets are pillows.

II. Some pillows are the beds.

III. Some beds are blankets

a. Only either I or II follows

b. Only I and either II or III follow

c. Only III and either I or II follow

d. All I, II and III follow

e. None of these

17. Statements: Some pictures are frames. Some frames are idols. All idols are curtains.

Conclusions: I. Some curtains are pictures.

II. Some curtains are frames.

III. Some idols are frames.

a. Only I and II follow

b. Only II and III follow

c. Only I and III follow

d. All follow

e. None of these

18. Statements: Some rats are cats. Some cats are dogs. No dog is cow.

Conclusions: I. No cow is cat.

II. No dog is rat.

III. Some cats are rats.

a. None follows

b. Only I and II follow

c. Only II and III follow

d. Only III follows

e. All I, II and III follow

19. Statements: Some uniforms are covers. All covers are papers. All papers are bags.

Conclusions: I. All covers are bags.

II. Some bags are covers, papers and uniforms.

III. Some uniforms are not papers.

a. Only I follows

b. Only I and II follow

c. Only III follows

d. All I, II and III follow

e. None of these

Directions (Questions 20 to 25): In each of the following questions, three statements are given followed by four conclusions numbered I, II, III and IV. You have to take the given statements to be true even if they seem to be at variance with commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

20. Statements: All pencils are birds. All birds are skies. All skies are hills.

Conclusions: I. All pencils are hills.

II. All hills are birds

III. All skies are pencils.

IV. All birds are hills.

a. Only I and II follow

b. Only I and III follow

c. Only III and IV follow

d. All follow

e. None of these

21. Statements: All needles are threads. All threads are boxes. All trees are boxes.

Conclusions: I. No needle is tree.

II. Some trees are threads.

III. Some boxes are needles.

IV. Some trees are needles.

a. None follows

b. Only either I or IV follows

c. Only either I or IV, and II follow

d. Only III follows

e. Only either I or IV, and III follow

22. Statements: All jungles are buses. All books are buses. All fruits are books.

Conclusions: I. Some fruits are jungles.

II. Some buses are books.

III. Some buses are jungles.

IV. All fruits are buses.

a. Only I, II and III follow

b. Only I, II and IV follow

c. Only II, III and IV follow

d. All follow

e. None of these

23. Statements: Some spoons are bowls. All bowls are knives. All knives are forks.

Conclusions: I. All spoons are forks.

II. All bowls are forks.

III. Some knives are bowls.

IV. Some forks are spoons.

a. Only II and III follow

b. Only II and IV follow

c. Only III and IV follow

d. All follow

e. None of these

24. Statements: All players are spectators. Some spectators are theatres. Some theatres are dramas.

Conclusions: I. Some dramas are spectators.

II. Some players are dramas.

III. Some theatres are players.

IV. All spectators are players.

a. None follows

b. Only I and III follow

c. Only II follows

d. Only II and IV follow

e. All follow

25. Statements: All benches are desks. Some desks are roads. All road are pillars.

Conclusions: I. Some pillars are benches.

II. Some pillars are desks.

III. Some roads are benches.

IV. No pillar is a bench.

a. None follows

b. Only either I or IV, and III follow

c. Only either I or IV follows

d. Only either I or IV, and II follow

e. All follow

Complete Answer key

All the Best!!!!

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