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SYLLOGISM

NOTE:

‣ Restatements always false.

‣ If any conclusion is false in any one diagram (B.D + P.D), that conclusion is always false.

‣ If any conclusion is true in all the diagrams (B.D + P.D), that conclusion is always true.

‣ If statement/ statements are in +VE, conclusions are in –VE: then that –VE conclusions are always false (VISE-VERSA).

 

ALL Statements: All A are B.
                     All B are C.

 

Conclusions:

1. All A are B (False)

2. All A are C (True)

3. All B are C (False)

4. All C are A (False)

5. All C are B (False)

6. All B are A (False)

 

Conclusions:

1. Some A are B (True)

2. Some A are C (True)

3. Some B are C (True)

4. Some C are A (True)

5. Some C are B (True)

6. Some B are A (True)

 

Conclusions:

1. Some A are not B (False)

2. Some A are not C (False)

3. Some B are not C (False)

4. Some C are not A (False)

5. Some C are not B (False)

6. Some B are not A (False)

 

Conclusions:

1. No A are B (False)

2. No A are C (False)

3. No B are C (False)

4. No C are A (False)

5. No C are B (False)

6. No B are A (False)

 

SOME Statement: Some A are B

Basic diagram:

 

Possible diagrams:

 

Conclusions:

1. All A are B (False)

2. All B are A (False)

3. Some A are B (False)

4. Some B are A (True)

5. No A is B (False)

6. No B is A (False)

7. Some A are not B (False)

8. Some B are not A (False)

 

NO Statement: No A is B.

 

Conclusions:

1. All A are B (False)

2. All B are A (False)

3. Some A are B (False)

4. Some B are A (False)

5. No A is B (False)

6. No B is A (True)

7. Some A are not B (True)

8. Some B are not A (True)

 

SOME NOT Statement: Some A are not B

 

Conclusions:

1. All A are B (False)

2. All B are A (False)

3. Some A are B (False)

4. Some B are A (False)

5. No A is B (False)

6. No B is A (False)

7. Some A are not B (False)

8. Some B are not A (False)

 

EITHER OR CASE Conditions:

‣ Given 2 conclusions must be false individually.

‣ Elements must be same in both the conclusions.

‣ Complimentary pair must be available in both the conclusions.

 

SPECIAL CASES

 

Conclusions:

I. No A is C (True)

II. No C is A (True)

III. Some A are not C (True)

IV. Some C are not A (True)

 

3. Statements:

All A are B. No A is C.

 

Conclusions:

I. Some B are not C (True)

II. Some C are not B (False)

 

POSSIBILITY CASE

1. Statements:  All A are B.

                          Some B are C.

                         No C is D.

 

Conclusions:

I. Some B’s being D’s is a possibility (True)

II. All A’s being C’s is a possibility (True)

III. All D’s being A’s is a possibility (True)

IV. Some C’s being B’s is a possibility (False)

Note: Existing relations or Established relations are always FALSE in Possibility conclusions.

 

2. Statements: No A is B.

                         All B are C.

                         Some C are D.

 

Conclusions:

I. All C’s can be A’s (False)

II. All A’s can never be D (False)

III. Some B ‘s can be D’s (True)

IV. There is possibility that Some C’s are A’s (True)

V. There is possibility that Some D are C (False)

 

 

Model Questions

Directions (Q.1-3): In each of the questions below are given three statements followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance from 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.

 

Give Answer:

A) If only Conclusion I follows

B) If only Conclusion II follows

C) If either Conclusion I or Conclusion IIfollows

D) If neither Conclusion I nor Conclusion IIfollows

E) If both Conclusion I and II follows

 

1. Statements: Some Dares are Dream.

                         All Dreams are Real.

                         No Real is Fake.

Conclusions:

I. Some Dreams are Fake.

II. All dream is not fake.

 

2. Statements: No Rain is Game.

Some Games are Chain.

No Chain is Lane.

Conclusions:

I. Some Chains are not Rain.

II. Some Games are Lane.

 

3. Statements:   Some Movie are Ticket.

                           No Ticket is Popcorn.

                           Some Popcorn is Burger.

Conclusions:

I. Some Movies are Burger.

II. Some Burgers are not Movie.

 

4. Statements:  Some Bag is Hot.

                          No Hot is Cake.

                          All Cakes are Milk.

Conclusions:

I. Some Bag is not Cakes.

II. Some Hots can be Milk.

III. Some Milk is not Hot.

 

Give Answer:

A) If only conclusion II follows

B) If both conclusions II and III follow

C) If both conclusions I and III follow

D) If both conclusions I and II follow

E) If all conclusions follows

Key With Explanations

 

Directions (1 - 10): In each questions below are given some statements followed by two conclusions I and II. You have to take given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follow/s from the given statements, disregarding commonly known facts. Read both the conclusions and give answer as -

1) If only conclusion I follows.

2) If only conclusion II follows.

3) If either conclusion I or II follows.

4) If neither conclusion I nor II follows.

5) If both conclusions I and II follow.

 

1. Statements: All mobiles are androids.

                          No android is a phone.

Conclusions: I. Some mobiles are not phones.

                      II. No phone is a mobile.

Ans: Both conclusions I and II follow.

 

Explanation:

                             

 

2. Statements: Some nails are pins.

                          Some pins are fingers.

Conclusions: I. No finger is a nail.

                      II. Some nails are fingers.

Ans: Either I or II follows.

 

Explanation:

                Basic diagram                                                 Alternate diagram                   

 

 

3. Statements: Some cranes are ducks.

                           No duck is a peacock.

Conclusions: I. No peacock is a crane.

                      II. Some peacocks are cranes.

Ans: Either I or II follows.

 

Explanation:

                     Basic diagram                                                       Alternate diagram
     

 

4. Statements: No chair is a glass.

                          All glasses are tables.

Conclusions: I. All tables are chairs.

                      II. Some tables are not chairs.

Ans: Only conclusion II follows.

 

Explanation:

When no table is a chair - definitely 'Some tables are not chairs' can be concluded. But this negative can conclusion in this question cannot have its complementory Conclusion (i.e. - All tables are chairs) because the first statement conditions get violated.

 

5. Statements: All cinemas are films.

                           All films are movies.

Conclusions: I. Some movies are cinemas.

                      II. All cinemas are movies.

Ans: Both conclusions I and II follow.
 

Explanation:
                                  

 

6. Statements: All friends are officers.

                          Some relatives are friends.

    Conclusions: I. No officer is a relative.

                         II. Some relatives are officer.

Ans: Only conclusion II follows.

Explanation:

 

7. Statements: Some girls are engineers.

                          Some engineers are teachers.

                          All teachers are politicians.

Conclusions: I. No politician is a girl.

                      II. Some politicians are engineers.

Ans: Only conclusion II follows.

Explanation:

In this question for 'No politician in a girl' gets its Complementary Conclusion i.e. Some Politicians are girls. Since it is not given, the given negative Conclusion become invalid.

see the alternate picture.

 

8. Statements: All fingers are rings.

                           No ring is a chain.

                          Some bags are rings.

Conclusions: I. No bag is a chain.

                      II. Some bags are chains.

Ans: Either I or II follows.

Explanation:

                     Basic diagram                                                     Alternate diagram
          

 

9. Statements: All numbers are digits.

                           Many digits are dots.

                           No dot is a light.

Conclusions: I. Some dots are numbers.

                      II. Some lights are digits.

Ans: Neither conclusion I nor II follows.

Explanation:
                     Basic diagram                               
              

 

10. Statements: All songs are smiles.
                             All smiles are lives.
                             No life is a cinema.
Conclusions: I. No cinema is a song.
                      II. No smile is a cinema.
Ans: Both conclusions I and II follow.

 

Explanation:
   

 

 Only a Few Type
“Only a few” means “conditional some”. “Only a few” means is the combination of “some” and “someb not”. Ex: Only a few A are B means Some A are B and Some A are not B.

Conclusions:
1. Some B are not A (False)
2. All B’s being A’s is a possibility (True)
3. All A’s being B’s is possibility (False)


Directions (Q.1 – 10): In the questions below are given some statements followed by some conclusions. You have to take the given statements to be true even if they seem to be in variance
with 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:
   Only a few river is ocean.
   Some ocean is pond.
   No pond is sea.
   All sea is lake.
Conclusions:
   I. All river being ocean is a possibility.
   II. Some lake being ocean is a possibility.
   III. Some pond is lake.
a) Only conclusion I follows.
b) Both conclusion I and II follow.
c) Only conclusion II follows.
d) Both conclusion II and III follow.
e) None of the above
Explanation:


2. Statements:

   No fruit is vegetable.
   Only a few vegetable is mango.
   No mango is grape.
   Some grape is orange

Conclusions:
  I. No orange is vegetable.
  II. Some fruit is mango.
  III. All vegetable being grape is a possibility.
a) Only conclusion III follows.
b) Both conclusion II and III follow.
c) Only conclusion I follows.
d) Both conclusion I and II follow.
e) None of the above
Explanation:


3. Statements:
  Only a few red is yellow.
  No yellow is blue.
  Only a few blue is green.
  Some green is pink.
Conclusions:
  I. All red being blue is a possibility.
  II. Some pink being blue is a possibility.
  III. Some yellow is pink.
a) Only conclusion II follows.
b) Both conclusion I and II follow.
c) Only conclusion III follows.
d) Both conclusion II and III follow.
e) None of the above
Explanation:


4. Statements:
   Only a few boy is girl.
   Some girl is man.
   Only a few man is woman.
   No woman is kid.
Conclusions: I. Some girl is not boy is a possibility.
  II. Some woman is not man.
  III. Some kid being girl is a possibility.
  a) Only conclusion I follows.
b) Both conclusion I and II follow.
c) Only conclusion II follows.
d) Both conclusion I and III follow.
e) None of the above
Explanation:


5. Statements:

  All square is line.
  Some line is circle.
  Only a few circle is oval.
  No oval is point.
Conclusions:
  I. No square is circle.
  II. All oval being circle is a possibility.
  III. Some point is line.
a) Only conclusion II follows.
b) Both conclusion I and II follow.
c) Only conclusion III follows.
d) Both conclusion II and III follow.
e) None of the above
Explanation:
 

                                       

 6. Statements:
   Only a few doctor is engineer.
   All engineer is developer.
   Some developer is tester.
   Only a few tester is trainer.
Conclusions:
   I. Some developer is  trainer.
  II. Some engineer being tester is a possibililty.
  III. Some developer is docter.
a) Both conclusion II and III follow.
b) Only conclusion III follows.
c) Only conclusion I follows.
d) Both conclusion I and II follow.
e) None of the above
Explanation:


7. Statements:
  Only a few keyboard is laptop.
  Some laptop is monitor.
  No monitor is IC.
Conclusions:
  I. Some keyboard is not laptop.
  II. All laptop being IC is a possibility.
a) Only conclusion I follows.
b) Only conclusion II follows.
c) Both conclusion I and II follow.
d) Neither conclusion I nor conclusion II followss.
e) None of the above
Explanation:


8. Statements:

   All summer is winter.
  Only a few winter is autumn.
  No autumn is climate.
  Conclusions:
  I. Some autumn is not winter is a possibility.
  II. Some summer is autumn.
a) Both conclusion I and II follow.
b) Only conclusion II follows.
c) Only conclusion I follows.
d) Neither conclusion I nor conclusion II follow.
e) None of the above
Explanation:


9. Statements:

  No Hindi is English.
  Only a few English is Science.
  No Science is Maths
Conclusions:
  I. No English being Science is a possibility.
  II. Some Hindi being Maths is a possibility.
a) Only conclusion I follows.
b) Both conclusion I and II follow.
c) Only conclusion II follows.
d) Neither conclusion I nor conclusion II follows.
e) None of the above
Explanation:


10. Statements:

  No table is chair.
  No chair is bench.
  Only a few bench is box.
Conclusions:

  I. Some box being table is a possibility.
  II. All box being bench is a possibility.
a) Only conclusion I follows.
b) Both conclusion I and II follow.
c) Only conclusion II follows.
d) Neither conclusion I nor conclusion  II follows.
e) None of the above
Explanation:

 


 Directions (Q.11 – 12): In the questions below are given some statements followed by some conclusions. You have to take the given statements to be true even if they seem to be in variance with
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.
11. Statements:
  Only few table is bench.
  No bench is desk.
  All desk is chair.
Conclusions:
  I. All table being bench is a possibility.
  II. Some chair being bench is a possibility.
a) Only conclusion I follows.
b) Only conclusion II follows.
c) Both conclusion I and II follow.
d) Neither conclusion I nor conclusion II follows.
e) None of the above
Explanation:

 

12. Statements:

  No floor is balcony.
  Some balcony is wall.
  Only few wall is door.
Conclusions:
  I. All wall being floor is a possibility.
  II. Some door is balcony.
a) Only conclusion I follows.
b) Only conclusion II follows.
c) Both conclusion I and II follow.
d) Neither conclusion I nor conclusion II follows.
e) None of the above
Explanation:

some more

Directions (Qs. 1 - 18): In each of the following questions, two statements are followed by two conclusions numbered I and II. You have to take the two given statements to be true even if they seem to be at variance with the commonly known facts and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts.
Mark your answer as:
a) If only conclusion I follows
b) If only conclusion II follows
c) If neither I nor II follows
d) If both I and II follow

1. Statements: Some rooms are stones. All stones are radios.
Conclusions: I. Some rooms are radios.
II. Some rooms are not radios. 
Sol: 

Depicting the first statement        Incorporating the second statemen
Only conclusion I is valid. Conclusion II is incorrect because of the possibility where the set of ‘rooms’ can be a subset of the set of ‘radios’ (second illustration).
Ans: a 

2. Statements: Some gowns are shirts. Some shirts are trousers.
Conclusions: I. Some gowns are trousers.
II. Some trousers are shirts.
Sol: G = Gowns, S = Shirts, T = Trousers

Only conclusion II is valid. Conclusion I cannot be definitely concluded because there might be no interaction between the set of ‘gowns’ and ‘trousers’ (T1).
Ans: b 

3. Statements: Some books are cups. Some cups are boxes.
Conclusions: I. Some books are boxes.
II. All boxes are books.

4. Statements: Some frogs are croaks. All frogs are big.
Conclusions: I. Frogs, which are not croaks, are big.
II. All Frogs, which are big, are not croaks.
Sol: Depicting the         Incorporating the second statement

Conclusion I is false because as per statement I, all frogs are big and not only the set which are ‘not croaks’. According to set B3, all frogs are big and some of them are croaks. So, conclusion II is also false.
Ans: c 

5. Statements: All trucks are flies. Some scooters are flies.
Conclusions: I. All trucks are scooters.
II. Some scooters are not flies. 

According to set S1, no truck is a scooter. Hence, conclusion I is not true. Conclusion II is invalid because the set of ‘flies’ can be a subset of the set of ‘scooters’ (S3). Hence, neither of the conclusion follows.
Ans: c 

6. Statements: All businessmen are hardworking men. No hardworking men are superstitious.
Conclusions: I. No businessmen are superstitious.
II. Some superstitious are not businessmen.
Sol: BM = Businessmen, S = Superstitious, HM = Hardworking Men

‘Businessmen’ and ‘Superstitious’ are disjoint sets. If ‘no superstitious are businessmen’, then ‘superstitions are not businessmen’ is also true. Both I and II follow. Hence, option (d) is correct.
Ans: d

7. Statements: All educated people are newspapers. Avi is not a newspaper.
Conclusions: I. Avi is not an educated person.
II. No newspapers are educated people.
Sol: EP = Educated People

Conclusion I follows but conclusion II does not follow. Hence, option 'a' is correct.
Ans: a 

8. Statements: All poets are authors. All singers are authors.
Conclusions: I. All singers are poets.
II. Some authors are not singers.
Sol:

None of the conclusions follow. Conclusion I is incorrect because the set of ‘poets’ and ‘singers’ could be disjoint sets (S1). Conclusion II does not follow because there is a possibility that the set of ‘authors’ and the set of ‘singers’ overlap.
Ans: c

9. Statements: Some spoons are small. All smalls are big.
Conclusions: I. All bigs are small.
II. All smalls are spoons.
Sol:  Depicting the first statement       Incorporating the second statement

10. Statements: All emeralds are diamonds. Some diamonds are pearls.
Conclusions: I. Some pearls are emeralds.
II. All diamonds are pearls

None of the conclusions follow.
Ans: c 

11. Statements: Some rivers are lakes. All lakes are ponds.
Conclusions: I. All ponds are lakes.
II. Some rivers are ponds. 

Only conclusion II follows. Hence, option 'b' is correct.
Ans: b 

12. Statements: Some flies are ants. All insects are ants.
Conclusions: I. All ants are flies.
II. Some ants are insects. 

Only conclusion II is true. Hence, option 'b' is correct.
Ans: b 

13. Statements: All planets are moons. All moons are suns.
Conclusions: I. All moons are planets.
II. All planets are suns. 

Only conclusion II follows. Hence, option 'b' is correct.
Ans: b 

14. Statements: All monkeys are dogs. All dogs are cats.
Conclusions: I. All monkeys are cats.
II. All cats are monkeys. 
Sol:  Depicting the           Incorporating the second statement
     first statement 

Only conclusion I is true. Hence, option 'a' is correct.
Ans: a 

15. Statements: All tubes are handles. All cups are handles.
Conclusions: I. All cups are tubes.
II. Some handles are not cups. 

Conclusion I does not follow as sets in C1 and C2 are not subsets of the set, ‘tubes’. Conclusion II is incorrect because the set of ‘cups’ and the set of ‘handles’ may overlap. Hence, option 'c' is correct.
Ans: c 

16. Statements: All books are cakes. All lamps are cakes.
Conclusions: I. Some lamps are books.
II. No lamp is book. 

Set L1 shows that conclusion I can be false and sets L2 and L3 show that conclusion II may be false. Hence, neither conclusion I nor II is correct.
Ans: c 

17. Statements: All flowers are stems. All stems are roots.
Conclusions: I. All roots are flowers.
II. All stems are flowers. 

Neither conclusion I nor II follows.
Ans: c 

18. Statements: Some rats are rabbits. All rats are mosquitoes.
Conclusions: I. Some mosquitoes are rabbits.
II. No rabbit is a mosquito.
Sol: R = Rats, Rb = Rabbits, M = Mosquito

Only conclusion I follows. Hence, option 'a' is correct.
Ans: a

 

SOME MORE

Directions (Q.1-2): In each of the following questions, two statements are followed by two conclusions numbered I and II. You have to take the two given statements to be true even if they seem to be at variance with the commonly known facts and then decide which of the given conclusions logically follows from the given statements, disregarding commonly known facts. Mark your answer as:
a) If only conclusion I follows 
b) If only conclusion II follows
c) If neither I nor II follows
d) If both I and II follow

1. Statement: All fans are cups.
       All cups are pillows.
Conclusions: I. All fans are pillows.
       II. All pillows are fans.

Only conclusion I follows.
Ans: a 

 

2. Statements: Komal Thakur is brilliant.
Komal Thakur is a woman.
Conclusions: I. Woman is brilliant.
II. Komal Thakur is brilliant because she is a woman. 

Neither conclusion I nor II follows. 
Ans: c 

 

Directions (Q.3-7): In each of the following questions, three statements and two conclusions are given. Your task is to find out which of the conclusions can be drawn from the given statements. Mark your answer if: 
a) If only conclusion I follows
b) If only conclusion II follows
c) If neither conclusion I nor II follows
d) If both conclusions I and II follow
3. Statements: Some cups are plastic.
         Some plastics are pens. Some pens are papers.
Conclusions: I. Some cups being papers is a possibility.
         II. All plastics are pens. 

Ans: a

 

4. Statements: All teachers are professors.
       All professors are advocates. All advocates wear black coat.
Conclusions: I. All advocates being teachers is a possibility.
       II. All teachers wear black coat.

 

5. Statements: Some snakes are venomous.
        All venomous are tigers.
        All tigers are lions.
Conclusions: I. All snakes are lions.
        II. All snakes are tigers. 

 

6. Statements: Some students are geniuses.
       Some geniuses are clever.
       Some clever are risk takers.
Conclusions: I. Some geniuses being risk takers are a possibility.
       II. All students are risk takers. 

 

7. Statements: Some poets are authors.
       All authors are dancers.
       All dancers are artists.
Conclusions: I. Some authors are artists.
       II. Some poets are artists. 

Posted Date : 24-04-2021

 

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