Campus Recruitment – Logical Reasoning – Syllogisms

Campus Recruitment – Logical Reasoning – Syllogisms

Concepts

Questions on syllogism contains statements followed by conclusions. You have to analyze the given statements carefully and find which of the conclusions logically follow.

Each statement of syllogism contains of three parts. They are, subject, predicate and copula.
Subject is that about which something is said.
Predicate is that part of the statement that which affirms is denied about the subject.
Copula is the word of the statement which denotes the relation between the subject and predicate.
Example: Consider the statement, ‘woman is tasted’. Here an information about woman is given. So, woman is the subject, ‘talented’ is the quality affirmed for this subject. So it is the predicate, ‘is’ denotes the relation between subject and predicate. So, it is copula.

Here we will discuss three types of methods to solve the questions on syllogism.
1) Diagrammatic method
2) Rules and Application method
3) Numbering and Apply method

1) Diagrammatic Method:
To solve the syllogism questions in this method, you have to represent the given statements in the form of a diagram.
fn syllogisms, frequently we come across the terms like all, some and no, not etc.
Example: 1) All papers are pens.
If the above statement are represented in a diagram, papers will be in inner circle and pens will be in outer circle, i.e.

2) Some papers are pens.

3) No paper is pen.
‘no’ indicates there is no relations exists between subject and predicate of the given statement. Hence, the two circles will not meet each other.

Example: Statements: Some Note books are books All books are papers
Conclusions: I. Some Notebooks are papers
II. No papers is notebook
Explanation: The possible Venn diagram for the given statements is as follows:

From the given statements, statement-I follows from the above diagram but statement-II does not follow.

2) Rules and Application Method:
The following rules are very useful while solving problems using this method.

Implication Statements:
1) All -»Some
If ‘all A’s are B’s’ then ’some A’s are B’s’ is also true.
2) Some <-> Some
If ‘some cats are rats’ then ‘some rats are cats’ is also true.
3) No <-> No
If ’no car is bus’ then ‘no bus is car’ is also true.
Note: For either-or option: If one conclusion is positive {i.e. starts with all/ some) and the other conclusion is negative (i.e. starts with no) and if they both have same objects as that of the given statements then the answer will be those two conclusions with either-or words.

Example: 1) Statements: Some keys are locks All locks are doors
Conclusions: I. All keys are doors
II. Some keys are doors
III. Some keys are not doors
a) only conclusion-(I) follows
b) only conclusion-(II) follows
c) only conclusion-(III) follows
d) both conclusion-(I) and (III) follows
e) None of the given conclusions follow
Explanation:
Step-1: Compare special words in both the statements.
i.e. some + all. Then, from the rule, some + all -> some.
Step-2: Compare predicate of the first statement and subject of the second statement. If both are same then cancel them and deduce a new conclusion.

‘some keys are doors’ is there in conclusion-(II). So, only conclusion-(II) follows. Hence, option-b is correct.

Note: From the given two statements if subject of the first statement and predicate of the second statement are not same, then it is not possible to deduce any conclusion from the two statements.

2) Statements: All bags are books
All pens are pencils
Conclusions: I. All bags are pencils
II. Some bags are pens
III. All pens are books
a) only conclusion-(I) follows
b) only conclusion-(II) follows
c) only conclusion-(III) follows
d) no conclusion follows
Explanation: Since the subject of the first statement and predicate of the second statement are not same, we cannot apply any rule. Hence, no conclusion follows.

3) Numbering and Apply Method:
The following rules are also very useful while solving the problems in this method.

Positive ->some/ all; Negative -> no/ some-not

Direct Relation: If any conclusion is/are directly derived from any of the given statement then it is called direct relation.
Indirect Relation: If the conclusion is not directly derived from any of the given statements then it is called indirect relation.
Consider the below value table which helps in solving the problems in this method.
Value Table:

Note: Consider the values given for the words in the statements as income. And values given for the words in the conclusions as expenditure.
Example: Statements: Some notebooks are books
All books are papers
Conclusions: I. Some notebooks are papers
II. No papers is notebook
Using the above value table we can number subject and predicate parts of the given statements and conclusions as shown below.

Steps to Solve:
Step-1: Observe the statements and conclusions using positive and negative table. If it is applicable then only go to the next step, else conclude.
Step-2:Assign the values to statements and conclusions using value table.
Step-3: Check every conclusion whether it has direct relation with the given statements. If yes go to step-4 else go to step-5.
Step-4: If the conclusion has direct relation then, compare total income and expenditure of subject and predicate separately and check if income ≥ expenditure.If both subject’s and predicate’s income ≥ expenditure then that conclusion is said to be true.
Step-5: If no direct relation exists between subject and predicate of any conclusion, then check which two statements has to be combined to get that particular conclusion. Then find the common word in those statements. Common word must have at least one value as 100. If Income of every word ≥ Expenditure of every word, then that conclusion is true.
Lets apply these method to an example.

Example: Statements: All pens are roads All roads are houses
Conclusion: I. All houses are pens
II. Some houses are pens
Explanation:
Step-1: The two given statements are positive. So, conclusions are also positive. (positive +positive = positive)
Step-2: Assign the values using value table.

Step-3: Consider conclusion-(I). It does not have direct relation to any of the given statements. We need to combine given two statements to get conclusion-(I). Now, check if any common word exist between the two statements and also the common word should have at least one value as 100.
Here the common word ‘road’ in both the statements. And it has one value as 100 in second statement.
Now, calculate income from statements and expenditure from conclusions.

From Conclusion-(I):
Income of houses = 50 and expenditure of houses = 100
Income < Expenditure Income of pens = 100 and expenditure of pens = 50. Income > Expenditure
In the first case, income < expenditure. In order for a conclusion to be valid, income should always be > expenditure. So, conclusion-(I) is invalid.

From Conclusion-(II):
Income of houses = 50 and expenditure of houses = 50.
Income > Expenditure
Income of pens = 100 and expenditure of pens = 50.
Income > Expenditure.
In both the cases, income > expenditure.
So, conclusion-(II) is valid.
Therefore, only conclusion-(II) follows.

Exercise

Directions(l-4): In each question below there are two statements followed by two conclusions numbered (I) and (II). You have to assume the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the two given statements and give your answer as
a: If only conclusion-(I) follows
b: If only conclusion-(II) follows
c: If either conclusion-(I) or (II) follows
d: If neither conclusion-(I) nor (II) follows
e: If both conclusion-(I) and (II) follow

1) Statements : Some flowers are birds
Some birds are cats
Conclusions: I. Some flowers are cats
II. No flower is cat

2) Statements: All pens are pencils
No pencil is cap
Conclusions: I. All caps are pencils
II. Some caps are pencils

3) Statements: Some teachers are players
No player is singer
Conclusions: I. Some teachers are singers
II. No singer is a teacher

4) Statements: No mobile is bag
Some bags are buckets
Conclusions: I. Some mobiles are buckets
II. Some buckets are not mobiles

Directions (5 – 8): Read the given statements carefully and decide which of the conclusions logically follow. And give answer as
a: If only conclusion-(I) follows
b: If only conclusion-(II) follows
c: If only conclusion-(III) follows
d: If either conclusion-(I) or (II) follows
e: If neither conclusion-(I) nor (II) follows
f: If only conclusion-(I) and (III) follows
g: If none of the given conclusions follow

5) Statements: Some eye drops are ear drops
All eye drops are liquids
Some liquids are drinkable
Conclusions: I. Sortie eye drops are drinkable
II. Some ear drops are drinkable
III. All liquids are eye drops

6) Statements: Nail polish is a cosmetic
No cosmetic is powder
Some powders are medicine
Conclusions: I. Some powders are cosmetic
II. Some medicine are nail polish
III. Some cosmetic are nail polish

7) Statements: All scales are pots
Some pots are bowls
All pots are rats
Conclusion: I. All scales are rats
II. Some scales are bowls
III. Some pots are rats

8) Statements: Some mobiles are tablets
All tablets are laptops
No mobile is chalk
Conclusions: I. Some mobiles are laptops
II. Some tablets are chalks
III. All mobiles are tablets

Directions (9 -12): Read the given statements carefully and decide which of the conclusions logically follow. And give answer as
a: If only conclusions-(I) and (II) follow
b: If only conclusion-(III) and (IV) follow
c: If only conclusions-(I) and (III) follow
d: If only conclusions-(II) and (IV) follow
e: If either conclusion-(I) or (III) follows
f: If either conclusion-(II) or (IV) follows
g: If none of the given conclusions follow

9) Statements: Some carpets are books
All books are pens
Some pens are carbons
All carbons are notebooks
Conclusions: I. Some carbons are carpets
II. Some carbons are books
III. Some pens are carpets
IV. Some notebooks are pens

10) Statements: All apples are tomatoes
All tomatoes are ladyfingers
All ladyfingers are oranges
Some oranges are bananas
Conclusions: I. Some oranges are tomatoes
II. All tomatoes are apples
III. Some apples are oranges
IV. All ladyfingers are apples

11) Statements: Some cool drinks are juices
Some juices are bags
All cats are mats
No cat is rat
Conclusions:I. At least some cool drinks are bags is a possibility
II. At least some mats are rats is a possibility
III. Some cool drinks are bags
IV. No cat is mat

12) Statements: All lids are caps
All caps are spoons
Some spoons are pens
Some pens are pencils
Conclusions:
I. Some caps are pens
II. All spoons are lids
III. At least some lids are pens is a possibility
IV. At least some pencils are caps is a possibility

Directions (13-24): Read the given statements carefully and decide which of the conclusions logically follow.
And give answer as
a: If only conclusion-(I) follows
b: If only conclusion-(II) follows
c: If only conclusion-(III) follows
d: If either conclusion-(I) or (II) follows
e: If neither conclusion-(I) nor (II) follows
f: If none of the given conclusions follows
g: If both conclusion-(I) and (II) follow
h: If both conclusion-(II) and (III) follow
i: If both conclusion-(III) and (IV) follow
j: If all the given conclusions follow

13) Statements: All men are doctors
All men are teachers
Conclusions: I. Some doctors are teachers
II. Some teachers are doctors

14) Statements: Some rivers are oceans
No ocean is well
Conclusions: I. Some rivers are not wells
II. No well is ocean

15) Statements: Some papers are chalks
No chalks are flowers
Conclusions: I. Some papers are flowers
II. No flower is paper

16) Statements: Some lights are candles
All candles are bulbs
Conclusions: I. All lights are bulbs
II. Some lights are bulbs
III. Some lights are not bulbs

17) Statements: Some dogs are cars
Some cars are horses
All horses are cows
Conclusions: I. Some cars are cows
II. Some cows are horses
III. Some dogs are horses

18) Statements: All tables are benches
No bench is chair
Conclusions: I. No table is chair
II. Some tables are benches
III. Some benches are tables

19) Statements: All dolls are cameras
Some cameras are chairs
All chairs are bells
Conclusions: I. Some bells are dolls
II. No bell is doll
III. All cameras are bells
IV. All chairs are cameras

20) Statements: All guns are sticks
All sticks are rods
Conclusions: I. Some rods are guns
II. All guns are rods
III. Some sticks are rods
IV. Some rods are not sticks

21) Statements: All tins are baskets
No basket is cot
Conclusions: I. No tin is cot
II. Some tins are cats
III. All baskets are tins
IV. Some cots are tins

22) Statements: Some pen drives are hard disks
All Hard disks are CD’s
Some books are CD’s
Conclusions: I. Some pen drives are CD’s
II. Some hard disks are pen drives
III. Some books are pen drives
IV. Some hard disks are books

23) Statements: Some fans are switches
All switches are lights
Some lights are mobiles
Conclusions: I. Some switches are mobiles
II. All fans are lights
III. Some fans are lights
IV. No switch is mobile

24) Statements: All scales are chocolates
All chocolates are sweet
Conclusions: I. All scales are sweet
II. No scale is sweet

25) Statements: Some players are singers
All singers are tall
Conclusions: I. Some players are tall
II. All players are tall

26) Statements: All bottles plastic
No plastic is stronger
Conclusions: I. No bottle is stronger
II. Some bottles are plastic

27) Statements: Some pens are goods
All goods are papers
Conclusions: I. No pen is paper
II. No pen is goods

28) Statements: No egg is black
No black is white
Conclusions: I. Some eggs are white
II. All whites are eggs

29) Statements: Some soaps are cinthol
No cinthol is bad
Conclusions: I. Some soaps are not bad
II. Some cinthols are soaps

30) Statements: Some schools are colleges
Some colleges are universities
All Universities are good
Conclusions: I. Some goods are schools
II. Some universities are schools

31) Statements: All cakes are breads
Some breads are fruits
Some fruits are biscuits
All biscuits are snacks
Conclusions: I. Some snacks are fruits
II. Some cakes are fruits

32) Statements: Some spoons are fruits
No fruit is red
Conclusions: I. Some fruits are spoons
II. No spoon is red

33) Statements: Some flowers are pillows
Some pillows are beds
All beds are fruits
No fruit is a bag
Conclusions: I. No bed is bag
II. Some flowers are bags
III. Some flowers are fruits

34) Statements: Some towers are pillars
Some pillars are buildings
All buildings are flats
No flat is house
Conclusions: I. No budding is house
II. Some towers are houses
III. Some towers are flats

35) Statements: All cups are saucers
Some glasses are plates
No glass is metal
Conclusions: I. Some plates are metal
II. Some cups are glasses
III. No plate is metal
IV. All metals are saucers

Explanations