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Syllogism Tips & Tricks and Practice Questions

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Syllogism is considered one of the confusing topics in Reasoning. The questions

along with the options look simple enough to lure candidates to answer them. But if the concepts are not clear, these questions can attract negative marking. You need

to be cautious enough to answer these questions. When it comes to Syllogism there

are various competitive exams which include this topic in their syllabus such as IBPS PO, Clerk, SBI Clerk, IBPS RRB etc.

Syllogism Tips & Tricks

Aspirants may follow these tips and tricks which may help them to master the

syllogs questions and will help them to solve these questions easily without any

hassle.

• Generally words like a few, atleast and all etc form the basis to solve such

questions, thus paying attention to these words is important while solving

syllogism questions. • Syllogism questions can be best solved with the help of Venn diagrams. This

basically makes it more clear and simplified which further helps to solve the

question easily. • The data which is mentioned in the question is to be followed only. While

solving such type of questions candidates must not assume anything and

should only follow what has been given. • Try and make out if there is any familiar concept.

• Also, try to attempt the questions in a sequential manner.

Let’s try to understand the different concepts of Syllogism with the help of the

Venn Diagram. Please note that we have exhausted all the possibilities where

only one statement is there (for eg. Some P are Q). But in multiple statements (for eg. 2. Some P are Q and some Q are R), there are many other options which

we’ll not be able to cover because of space constraints.



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1. Some P are Q

This is one of the most generalized statement. It says that some P are Q but

doesn’t really tell us how much of P (may be the complete Q is P) is Q. You need to think about all the probabilities when you see this statement.

Conclusions:

1. Some P are Q

2. Some Q are P

2. Some P are Q and some Q are R

Conclusions:



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1. Some P are Q

2. Some Q are P

3. Some Q are R

4. Some R are Q

Since there isn’t any connection mentioned between P and R so it’s not possible

to conclude anything about them. But between Some “P are R” and “None of P is R”, we know that either of these conclusions has to be true. Either P and R

will have a connection or it won’t have a connection.

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3. All P are Q

Conclusions:

1. All P are Q

2. Some P are Q

3. Some Q are P

4. All P are Q and all Q are R



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Conclusions:

1. All P are Q

2. All Q are R

3. All P are R

4. Some P are Q 5. Some Q are P

6. Some Q are R

7. Some R are Q 8. Some P are R

9. Some R are P

5. Some P are Q. All Q are R



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Conclusions:

1. Some P are Q

2. Some Q are P

3. All Q are R

4. Some Q are R

5. Some R are Q 6. Some P are R

7. Some R are P

6. All P are Q, Some Q are R



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Conclusions:

1. All P are Q

2. Some P are Q

3. Some Q are P 4. Some Q are R

5. Some R are Q

Since there isn’t any connection mentioned between P and R so it’s not possible

to conclude anything about them. But between Some “P are R” and “None of P is

R”, we know that either of these conclusions has to be true. Either P and R will have a connection or it won’t have a connection.

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7. All Q are P, All R are P



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Conclusions:

• All Q are P

• Some Q are P • Some P are Q

• All R are P

• Some R are P

• Some P are R

Since there isn’t any connection mentioned between Q and R so it’s not possible to conclude anything about them. But between "Some Q are R” and “None of Q is

R”, we know that either of these conclusions has to be true. Either Q and R

will have a connection or it won’t have a connection.

8. No P is Q



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Conclusions:

• No P is Q

• No Q is P

• Some P is not Q

• Some Q is not P

9. All P are Q, No Q is R

Conclusions:

• All P are Q

• Some P are Q



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• Some Q are P • No R is Q

• No Q is R

• Some R is not Q • Some Q is not R

• No R is P

• No P is R • Some R is not P

• Some P is not R

10. All P are Q, No P is R



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Conclusions:

• All P are Q

• Some P are Q • Some Q are P

• No P is R

• No R is P • Some P is not R

• Some R is not P

• Some Q is not R

10. Some P are Q, No Q is R

Conclusions:

• Some P are Q

• Some Q are P • No Q is R

• No R is Q

• Some R is not Q • Some Q is not R

• Some P is not R

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12. Some P are Q, No P is R

Conclusions:

• Some P are Q

• Some Q are P • No P is R

• No R is P

• Some P is not R • Some R is not P

• Some Q is not R

Scenarios of "Only" and "Only Few"

The concept of 'Only Few' and 'Only a Few' are the same.

Statements:

Only few A are B



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Some B are C

Conclusions:

I. All A being B is a possibility: Doesn’t Follow

OR

As only few A are B, all A cannot be B.

II. No A being B is a possibility: Doesn’t Follow

OR

Some A has to be B.

III. All B being A is a possibility: Follows



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OR

As there are two possibilities, all B may be A.

IV. Some A are not B: Follows

OR

As only few A are B, so some A are definitely not B.



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V. Some A not being B is a possibility: Doesn’t Follow

OR

Only few A are B, it means that some A are definitely not B and it is not a

possibility, it is definitely true.

VI. Some B are not A: Doesn’t Follow

OR

In 1st possibility, all B are A while in 2nd possibility, some B are not A.



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VII. Some B not being A is a possibility: Follows

OR

In 1st possibility, all B are A while in 2nd possibility, some B are not A.

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VIII. Some A are not C: Doesn’t Follow

OR



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All A are C is 1st possibility. So, it doesn’t follow.

Statements:

Only C are T (It means that all T are C and no other element is T, and

there will be no intersection)

Some C are B

Conclusions:

I. Some B can be T: Doesn’t Follow

No B is T.

II. All B can be C: Follows

As some C are B, all B can be C.

III. All C can be B: Doesn’t Follow

As T cannot be B, so all C cannot be B

IV. Some T not being C is a possibility: Doesn’t Follow and is false



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All T are C, so some T not being C is not at all possible.

V. No T is B: Follows

Only C are T, so T is not B.

Usage of ‘Possibility’ and ‘Can’

Sometimes, questions have the word possibility and can. Whenever you face this

kind of question, see if there is any statement which is outrightly negating it. If no negation is there, the possibility is definitely there. You can also remember the below

rules:

Statement: All P are Q

Conclusion:

• All Q being P is a possibility

• Some Q is not P is a possibility

Statement: Some P are Q



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Conclusion:


• All P being Q is a possibility • Some P is not Q is a possibility


Statement: Some P is not Q

Conclusion:


• No P is Q is a possibility • No Q is P is a possibility


• Some P are Q is a possibility

• Some Q are P is a possibility

Sample Questions for SBI Clerk 2020 Mains (With Explanatory Answers)

Question 6: In the question below there are four statements followed by three

conclusions I, II and III. You have to take the three 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 follows from the four statements

disregarding commonly known facts.

Statements:

No mobiles are laptops.

Only few laptops are computers.

Few computers are keyboards.

All keyboards are phones.

Conclusions:



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I. Some laptops are not keyboards.

II. Each computers may be mobiles

III. Mostly phones are computers

a. Both conclusion I and conclusion II follow.

b. Only conclusion III follows

c. Neither conclusion I nor conclusion II follows

d. Only conclusion II follows

e. None of the above

Answer: b

Solution:

Following figure can be formed:

OR



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From the figure, only conclusion III follows

Hence, option b.

Question 7: In the question 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.

Statements:

Only few rackets are handles.

At least some hats are handles.

No hat is beaker.

Conclusions:

I: All handles being beaker is not a possibility.

II: Mostly hats are rackets.

a. Only conclusion I follows

b. Only conclusion II follows

c. Either conclusion I or II follows

d. Both conclusion I and II follows

e. Neither conclusion I nor II follows

Answer: a

Solution:

The figure deduced from the statements,



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OR

So, only conclusion I follows.

Hence, option a.



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.

Statements:

Only maps are roads.

Some maps are tracks.



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No track is route.

Conclusions:

I: Some roads are routes.

II: Some maps are routes.






Answer: e

Solution:


OR



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Only maps are roads means nothing can be part of roads except maps.

So, neithe conclusion I nor conclusion II follows.

Hence, option e.



even if they seem to be at variance from commonly known facts and then decide

which of the given conclusions logically follows from the four statements disregarding commonly known facts.

Statements:

99% states are countries

No countries are continents

Every continents is islands

Mostly islands are towns

Conclusions:

I. Few countries being islands is a possibility.

II. No towns are continents

III. Mostly states are towns




d. Only conclusion I follows


Answer: d



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Solution:


OR

From the figure, only conclusion I follows

Hence, option d.



even if they seem to be at variance from commonly known facts and then decide

which of the given conclusions logically follows from the four statements


Statements:

12.86% ponds are rivers.

98% rivers are oceans.

Every oceans is lakes.

No lakes are waters.

Conclusions:



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I. Few ponds being lakes is a possibility.

II. No oceans are waters.

III. Mostly waters are rivers.




d. Only conclusion I follows


Answer: a

Solution:


OR



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From the figure, both conclusion I and conclusion II follow.

Hence, option a.

Sample Questions for IBPS RRB Clerk 2020 Prelims (With Explanatory

Answers)


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


Statements:

Only few books are papers.

No paper is novel.

Some novels are copies.

Conclusions:

I: Some papers are copies.

II: All copies are papers.






Answer: Answer: e

Solution:




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Therefore, neither conclusion I nor II follows.

Hence, option e.






Statements:

Only days are months.

No day is year.

Some years are decades.

Conclusions:

I: No decade is day.

II: Some months are decades.




d. Both conclusions I and II follow



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Answer: e Solution:


Therefore, neither conclusion I nor II follows. Hence, option e.





Statements:

Only few bats are balls.

Few balls are stumps.

No stump is pitch.

Conclusions:

I: Some balls are not pitches.

II: All bats are balls.








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Answer: a Solution:


Therefore, only conclusion I follows.

Hence, option a.



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


Statements:

All rum is whisky.

No whisky is beer.

Only beer is vodka.

Conclusions:

I: No rum is beer.

II: Some vodka may be whisky.






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Answer: Answer: a Solution:



Hence, option a.

Question 5: In the question below there are three statements followed by two

conclusions I and II. You have to take the three 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 follows from the four statements disregarding

commonly known facts.

Statements:

25.5% of stones are rocks.

None rock is sand.

Only sands are bricks.

Conclusions:

I. No rock is brick.

II. Some stones are sands.

a. Both conclusion I and conclusion III follow.

b. Only conclusion I follows





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Answer: b

Solution:


From the figure, only conclusion I follows.

Hence, option b.

Sample Questions for SBI PO 2020 Prelims (With Explanatory Answers)





Statements:

Only a few rides are trips.

No trip is mountain.

All mountains are trees.



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Conclusions:

I: Some trees are not trips.

II: All rides being trips is not a possibility.






Answer: d

Solution:


OR



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As, the part covering both mountains and trees will never be part of trips. So,

statement I must be true.

Also, all trips can be rides as shown in 2nd figure and vice versa is not possible.

So, statement II cannot be true.

Therefore, both conclusions I and II follow.

Hence, option d.


conclusions I and II. You have to take the three 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 follows from the three statements disregarding commonly known facts.

Statements:

Mostly pets are cats

Only cats are dogs

No cats are rabbits

Conclusions:

I. Some pets are rabbits.

II. All pets being rabbits is not a possibility.


b. Only conclusion I follows




Answer: d

Solution:




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OR

As, rabbits can’t be part of cats and some pets are cats. Therefore all pets cannot

be rabbits.

From the figure, only conclusion II follows.

Hence, option d.


conclusions I and II. You have to take the three 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 follows from the three statements disregarding

commonly known facts.

Statements:



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At least some petals are leaves.

All leaves are plants

No plant is seed

Conclusions:

I. All leaves may be seeds

II. Some petals are plants

a. Only conclusion II follows

b. None of the above


d. Both conclusion I and conclusion II follow.

e. Only conclusion I follows

Answer: a

Solution:


As, all leaves are plants and no plants are seeds then leaves cannot be part of

seeds. So, statement I is not possible.

From the figure, only conclusion II follows

Hence, option a.



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conclusions and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts.

Statements:

No box is bowl.

All bowls are cups.

Each cup is glass.

Conclusions:

I: All bowls are glasses.

II: Some cups are boxes.






Answer: a

Solution:




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OR


Hence, option a.



even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the four statements


Statements:

All watches are clocks.

Only clocks are mirrors.

Few clocks are walls.

No walls are glasses.

Conclusions:



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I. Few mirrors may be watches

II. Mostly walls being watches is a possibility

III. Some clocks are glasses.

a) Only conclusion II follows

b) Only conclusion III follows

c) Only conclusion I follows

d) Both conclusion I and III follow.

e) None of these

Answer: a

Solution:


OR

Only clocks are mirrors means than nothing can be part of mirror except clocks.



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From the figure, only conclusion II follows.

Hence, option a.



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