Aristotle introduced the concept of ‘Syllogism’. It denotes ‘inference’ or ‘deduction’. Syllogisms are an important part of almost every competitive exam and are included in the Reasoning section. Over the years syllogisms have become mystifying in nature and thus tricky to solve.
It is an important section of logical reasoning and hence, working knowledge of its rules is a must to solve the problems. The list of exams where the questions of syllogisms are asked includes CAPF, RRBs, SSC, SBI PO, SBI Clerk, SBI SO, IBPS PO, IBPS SO, IBPS Clerk etc. In this article, we will discuss given below points regarding Syllogism:
In the given below tabs are the links of Syllogism Quizzes and PDFs:
It is an important section of logical reasoning and hence, working knowledge of its rules is a must to solve the problems. The list of exams where the questions of syllogisms are asked includes CAPF, RRBs, SSC, SBI PO, SBI Clerk, SBI SO, IBPS PO, IBPS SO, IBPS Clerk etc. In this article, we will discuss given below points regarding Syllogism:
- Syllogism PDF
- Syllogism Quiz
- History of Syllogism
- Types of Syllogism Questions
- Concept of Syllogism
- Syllogism Complementary pair (Either or condition)
- Syllogism Concept of Only a few and Only
- Syllogism Questions and Answers
- High Level Syllogism Problems
- Syllogism Questions for Bank Exams
- Syllogism Questions for SSC Exams
In the given below tabs are the links of Syllogism Quizzes and PDFs:
Syllogism PDF:
Syllogism PDF Set 1
Syllogism Quiz
History of Syllogism:
The word syllogism is derived from the Greek word “syllogismos” which refers to “conclusion and inference”. They are a logical argument of statements where deductive reasoning is used to arrive at a conclusion.
Types of Syllogism Questions:
The questions asked in this section have two or more statements which are followed by two or more than two conclusions. One needs to find out which of these conclusions logically follow from the given statements. The statements are taken to be true even if they seem to disregard the commonly known facts.
Concept of Syllogism:
There are many ways in which questions of syllogisms can be solved. One of the most effective and efficient methods is using a Venn diagram. On the basis of the given statements, one can draw all the possible diagrams and then arrive at the solution from each of these diagrams separately. Finally, the answer which is common to all diagrams is taken to be as the correct one.
Statements of Syllogisms:
The questions of syllogisms can be divided into three main parts.
- Major premise
- Minor premise
- Conclusion
Example 1: All men are smart.
The minor premise is a specific example of the major premise.
Example 2: Ram is a man.
The conclusion is a specific statement which can logically follow both major and minor premise.
Example 3: Ram is smart.
A premise is a sentence which makes a statement and hence, it presents a relation between two or more terms. In case of logical deduction, any statement is termed as a premise.
For Example:
All doors are rods
No cloth is a clean
Some students are hostlers
Some red is not white
The following parts of a premise as explained below:
Subject: A subject is that part of the premise which is being talked about.
Predicate: A predicate is the part of the premise which shows what is affirmed or denied about the subject.
Qualifiers: It usually starts with words - Some, All, No, Some not.
The word ‘all’, includes synonyms such as Every, Any, Each.
The word ‘Some’ can also be replaced by – Many, Few, Most of, More, A little
The premise in a Syllogism:
They are divided into Universal and Particular statements and are also divided into positive and negative statements.
i. Universal positive: A premise of the form includes:
[All P are Q] is known as the universal positive proposition. A universal positive premise is denoted by “A”. For Example;
All peacock are tigers.
All cards are tigers.
ii. Universal negative: A premise in the form [No P is Q] is known as a universal negative premise. It is denoted by letter “E”.For example;
No student is lazy.
No car is box.
iii. Particular positive: A premise in the form [Some R are S] is called a particular positive premise. It is generally denoted by “I”. For example;
Some students are smart.
Some dogs are cats.
iv. Particular negative: A premise in the form [Some S are not P] is known as a particular negative premise. It is denoted by the “O”. For instance;
Some kids are not lazy.
Some bulbs are not yellow.
Inference or Conclusions in syllogisms:
In syllogism, there are two types of inferences, these are:
1. Mediate: In the mediate inference, the conclusion can be drawn from two propositions.
For example:
[All cats are lions] and [All lions are animals]. Then the conclusion – [All cats are animals] could be drawn from the given.
2. Immediate: When the conclusion can be drawn from only one given premise, it is known as immediate inference.
For example:
[All shirts are blue], then based upon this statement, the conclusion could be drawn – [Some blue are shirts].
This type of conclusions is known as immediate inference.
Rules for Deductions in Syllogisms:
- Every deduction requires three and only three distinct terms.
- If both the premises in the statements are negative, then No conclusion can be drawn.
- If both the premises are particular, then no conclusion can be drawn.
- The middle term in both the premises must be distributed at least once in the premises.
- If one premise is negative, the conclusion must be negative.
- If one proposition is particular, then the conclusion must be negative.
- No term can be distributed in the conclusion if it is not distributed in the premises.
There are three types of conclusion in Syllogism:
- Positive- when we are 100% sure.
- Negative- In this case, we are sure that it doesn’t result in occurrence.
- Possibility- In this, we are not 100% sure but a possible case may occur.
1. Positive conclusion:
Statements:
All medals are awards.
All rewards are medals.
Conclusions:
I. All rewards are awards.
II. All awards are medals.
A. if only conclusion I follows.
B. if only conclusion II follows.
C. if either conclusion I or conclusion II follows.
D. if neither conclusion I nor conclusion II follows.
E. if both conclusion I and conclusion II follow.
Solution:
All rewards are medals (A) + All medals are awards (A) = A + A = A = All rewards are awards.
Hence, conclusion I follows.
But, conclusion II does not follow.
Hence, option A is correct.
2. Negative conclusion:
Statements:
All windows are doors.
All entrances are windows.
No gate is a door.
Conclusions:
I. At least some windows are gates.
II. No gate is an entrance.
A. if only conclusion I follows.
B. if only conclusion II follows.
C. if either conclusion I or conclusion II follows.
D. if neither conclusion I nor conclusion II follows.
E. if both conclusion I and conclusion II follow.
Solution:
All entrances are windows (A) + All windows are doors (A) + [No gate is a door (E)] = No door is a gate (E) = A + E = E = No entrance is a gate.
Hence, conclusion II follows.
Again,
All window are doors (A) + [No gate is a door (E)] = No door is a gate (E) = A + E = E = No window is a gate.
Thus, conclusion I does not follow.
3. Possibility conclusion:
In syllogism, conclusion which is not 100% sure, it’s possibilities can happen i.e we are doubtful in saying it but possibility may occurs.
Statements:
Some balls are bats.
No bat is a wicket.
Conclusions :
I. Some wickets are not ball.
II. All wickets being ball is a possibility.
A. if only conclusion I follows.
B. if only conclusion II follows.
C. if either conclusion I or conclusion II follows.
D. if neither conclusion I nor conclusion II follows.
E. if both conclusion I and conclusion II follow.
Solution:
Some balls are bats (I) + No bat is a wicket (E) = I + E = O = Some balls are not wickets.
Hence, conclusion I does not follow. But the possibility in II exists. Thus, conclusion II follows.
Syllogism Complementary pair: (Either or condition):
Conditions of complementary pairs.
1. Some & No
Statements:
Some balls are bats.
No bat is a wicket.
Conclusions :
I. Some wickets are not ball.
II. All wickets being ball is a possibility.
A. if only conclusion I follows.
B. if only conclusion II follows.
C. if either conclusion I or conclusion II follows.
D. if neither conclusion I nor conclusion II follows.
E. if both conclusion I and conclusion II follow.
Solution:
Some balls are bats (I) + No bat is a wicket (E) = I + E = O = Some balls are not wickets.
Hence, conclusion I does not follow. But the possibility in II exists. Thus, conclusion II follows.
2. All & Some Not
Statements:
All stickers are cups.
No cup is a wire.
All wires are bulbs.
Conclusions:
I. All bulbs being cups is a possibility.
II. No sticker is a wire.
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 conclusions I and II follow
Solution:
No cup is a wire (E) + All wires are bulbs (A) = E + A = O* = Some bulbs are not stickers. Hence, conclusion I does not follows.
Again, All stickers are cups (A) + No cup is a wire (E) = A + E = E = No sticker is a wire. Hence, conclusion II follows.
Syllogism Concept of Only a few and Only:
1. Only a few: Means some but not all.
Statements :
Only a few teachers are doctors.
0% teachers are lawyers.
Conclusions :
I. All lawyers are teachers.
II. Some doctors are not lawyers.
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
E. if either conclusion I or II follows
Solution:
Checking C1: All lawyers are teachers.
Converse of S2 (No teachers are lawyers) ⇒ No lawyers are teachers.
Clearly, C1 doesn't follow.
Checking C2: Some doctors are not lawyers.
Using converse of S1 and S2, we get
Some doctors are teachers (I) + No teachers are lawyers (E) ⇒ Some doctors are not lawyers.
2. Only:
Statements:
Some balls are bats.
No bat is a wicket.
Conclusions :
I. Some wickets are not ball.
II. All wickets being ball is a possibility.
A. if only conclusion I follows.
B. if only conclusion II follows.
C. if either conclusion I or conclusion II follows.
D. if neither conclusion I nor conclusion II follows.
E. if both conclusion I and conclusion II follow.
Solution:
Some balls are bats (I) + No bat is a wicket (E) = I + E = O = Some balls are not wickets.
Hence, the conclusion I does not follow. But the possibility in II exists. Thus, conclusion II follows.
Syllogism Questions and Answers:
Question 1 :
Statements:
No cream is lotion.
Not a single lotion is oil.
Every oil is shampoo.
Conclusions:
I. Some shampoos which are oil are cream as well.
II. No cream is an oil.
A. Only C1 follows
B. Either C1 or C2 follows
C. Both C1 and C2 follow
D. None follows
E. None of these
Solution:
Checking C1:
Some shampoo which are oil are cream as well.
If we observe the given statements, we can find that in Statement 1 and 2, the middle term ‘lotion’ is distributed twice and therefore even after conversing either of the sentence we won’t be able to find a definite conclusion out of these two. Therefore, we can’t derive a definite relationship between ‘oil’ and ‘cream’.
C1 hence doesn’t follow.
Checking C2:
No cream is an oil.
Following the logic explained above, we can clearly say that C2 doesn’t follow either.
Between the two, none follow.
Option D is hence the correct answer.
Question 2:
Statements:
No laptop is apple.
Not a single apple is mobile.
Every mobile is tablet.
Conclusions:
I. Some tablets which are mobiles are laptops as well.
II. Some tablets are not apples..
A. Only C2 follows
B. Either C1 or C2 follows
C. Both C1 and C2 follow
D. None follows
E. None of these
Solution:
Checking C1:
Some tablets which are mobiles are laptops as well.
If we observe the given statements, we can find that in Statement 1 and 2, the middle term ‘apple’ is distributed twice and therefore even after conversing either of the sentence we won’t be able to find a definite conclusion out of these two. Therefore, we can’t derive a definite relationmobile between ‘mobile’ and ‘laptop’.
C1 hence doesn’t follow.
Checking C2:
Some tablets are not apples.
From S2 and S3,
Not a single apple is mobile (E) + Every mobile is tablet (A) = Some tablets are not apples.
Clearly, C2 follows.
Among all, only C2 follows.
Option A is hence the correct answer.
Question 3:
Statements:
A few balloons are not toys.
All toys are bear.
No bear is wild..
Conclusions:
I. No wild is a toy.
II. No balloon is wild..
A. Only C1 follows
B. Either C1 or C2 follows
C. Both C1 and C2 follow
D. None follows
E. None of these
Solution:
Checking C1:
No wild is a toy.
From S1 and S2,
All toys are bear (A) + No bear is wild (E) = No toy is wild or No wild is a toy.
C1 hence follows.
Checking C2:
No balloon is wild.
Clearly, S1 in which the class ‘balloons’ exists is an O type statement, we can’t derive a definite relationship of it with any other statement.
Clearly, C2 doesn’t follow.
Evidently, only C1 follows.
Option A is hence the correct answer.
Question 4:
Statements:
Some temples are churches.
No mosque is a church.
Some mosques are bells.
Conclusions:
I. All bells being temples is a possibility.
II. No church is a mosque.
III. All bells are mosques.
A. Only III follows
B. Only II follows
C. Only I and II follow
D. All follow
E. None of these
Solution:
Checking Conclusion I: All bells being temples is a possibility
If we observe the given statements, we can find that we are getting
Some temples are churches + Converse of S2 (No church is a mosque) = Some temples are not mosques.
Now, using the above derived conclusion and S3, we can’t deduce a definite conclusion between the classes ‘bells’ and ‘temples’. Clearly, possibility between these two does exist. Hence, C1 follows.
Checking Conclusion II: No mosque is a church
Converse of S2 = No mosque is a church
Clearly, C2 follows as well.
Checking Conclusion III: All bells are mosques
Converse of S3 = Some bells are mosques
Clearly, C3 doesn’t follow.
Option C is hence the correct answer.
Question 5:
Statements:
Some Litchi are Vanilla.
All Butterscotch are Vanilla.
Some Strawberry are Litchi.
Conclusions:
I. At least some Butterscotch being Litchi is a possibility.
II. All Strawberry being Vanilla is a possibility.
III. Some Litchi are not Strawberry.
A. Only I and II follow
B. Only III follows
C. Only II and III follow
D. Only I and III follow
E. None of these
Solution:
Given Statements:
Some Litchi are Vanilla.
All Butterscotch are Vanilla.
Some Strawberry are Litchi.
Given Conclusions:
I. At least some Butterscotch being Litchi is a possibility.
II. All Strawberry being Vanilla is a possibility.
III. Some Litchi are not Strawberry.
Checking Conclusions I and II: ‘At least some Butterscotch being Litchi is a possibility’ & ‘All Strawberry being Vanilla is a possibility’.
There is no negative statement. Thus the possibility can exist. Hence, conclusion I and II follow.
Checking Conclusion III: Some Litchi are not Strawberry
Again, Some Strawberry are Litchi (I) – conversion – Some Litchi are Strawberry (I). Hence, conclusion III does not follow.
Option A is hence the correct answer..
Question 6:
Statements:
No curtain is an element.
All elements are pillows.
Conclusions:
I. All pillows being curtains is a possibility.
II. Some elements are definitely not curtains.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either conclusion I or II follows
D. Both conclusions I and II follows
E. Neither conclusion I nor II follows
Solution:
No curtain is an element (E) + All elements are pillows (A) = E + A = O* = Some pillows are not curtains. Hence the possibility in I does not exist.
Again,
No curtain is an element (E) → conversion → No element is a curtain (E) → implication → Some elements are definitely not curtains. Hence II follows.
Therefore, option B is correct.
Question 7:
Statements:
No phone is an airplane.
All ships are airplanes.
Conclusions:
I. No ship is phone.
II. At least some airplanes are phones.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either conclusion I or II follows
D. Both conclusions I and II follows
E. Neither conclusion I nor conclusion II follows
Solution:
Using statement I and II, we get
All ships are airplanes + Converse of 'No phone is an airplane' = No ship is airplane.
Hence, conclusion I follows.
Using statement I, we get
Converse of 'No phone is an airplane' = No airplane is phone.
Hence, conclusion II doesn't follow.
Option A is hence the correct answer.
Question 8:
Statements:
Some questions are quizzes.
Some quizzes are not queries.
Conclusions:
I. All queries being quizzes is a possibility.
II. All quizzes being questions is a possibility.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either conclusion I or II follows
D. Both conclusions I and II follow
E. Neither conclusion I nor II follows
Solution:
Using statement II, we get
Some quizzes are not queries.
Here, if we observe we get to know that we aren't sure of any of the elements of class 'queries'. Therefore, "All queries being quizzes is a possibility". Hence, conclusion I follows.
Using statement II, we get
Some questions are quizzes.
Converse = Some quizzes are questions.
Now, if some quizzes are questions, what are the rest of the quizzes? They may be questions too or they may not be questions. Considering the former possibility, we can say that "All quizzes being questions is a possibility".
Option D is hence the correct answer.
High Level Syllogism Problems:
Question 1:
Statements:
A few daughters are not mothers.
All mothers are sisters.
No sister is a niece.
Conclusions:
I. No niece is a mother.
II. No daughter is a niece.
III. Some mothers are not daughters.
IV. Some nieces are both mothers and daughters.
A. Only C3 follows
B. Either C1 or C2 follows
C. Only C2 and C3 follow
D. All follow
E. None of these
Solution:
Checking C1: No niece is a mother.
From S1 and S2,
All mothers are sisters (A) + No sister is a niece (E) = No mother is a niece or No niece is a mother.
C1 hence follows.
Checking C2: No daughter is a niece.
Clearly, S1 in which the class ‘daughter’ exists is an O type statement, we can’t derive a definite relationship of it with any other statement.
Clearly, C2 doesn’t follow.
Checking C3: Some mothers are not daughters.
From S1,
A few daughters are not mothers.
But as conversion of an O type statement is not valid, C3 doesn’t follow either.
Checking C4: Some nieces are both mothers and daughters.
Following the logic explained C2, we can eliminate C4 as well.
Evidently, only C1 follows. Option E is hence the correct answer.
Question 2:
Statements:
Some SRKs are actors.
All actresses are actors.
No actor is musician.
Conclusions:
I. Some SRKs are actresses.
II. All musicians being actresses is a possibility.
III. No SRK is an actress.
IV. Some actors not being SRK is a possibility.
A. Only C2 follows
B. Either C1 or C3 and C2 and C4 follow
C. Only C2 and C4 follow
D. All follow
E. None of these
Solution:
Checking C1 and C3: ‘Some SRKs are actresses’ and ‘No SRK is an actress.’
In S1 and S2, we can observe that the middle term ‘actors’ is not distributed even once, a definite conclusion can’t be derived between these two. And C1 is an I type statement and C2 is an E type statement, they both form a complementary pair (E + I combination).
Therefore, either C1 or C3 follows.
Checking C2: All musicians being actresses is a possibility.
From S2 and S3,
All actresses are actors + No actor is musician = No actress is a musician.
Clearly, there is no possibility that exists between ‘actress’ and ‘musician’.
C2 hence doesn’t follow.
Checking C4: Some actors not being SRK is a possibility.
From S1,
Some SRKs are actors.
Converse of it = Some actors are SRK.
Now, if some actors are SRK, what are the other actors? They could be either SRK too or they could not be SRK.
Following the latter notion, we can say that ‘Some actors not being SRK’ is a possibility.
C4 hence follows.
Evidently, either C1 or C3 and C4 follow.
Clearly, none of these (option E) is the correct answer.
Question 3:
Statements:
No whale is shark.
Not a single shark is fish.
Every fish are deer.
Conclusions:
I. Some deer which are fish are whale as well.
II. No whale is a fish.
III. Some deer are not shark.
IV. No whale is a deer..
A. Only C3 follows
B. Only C1, C2 and C3 follow
C. Only C2 and C4 follow
D. All follow
E. None of these
Solution:
Checking C1: Some deer which are fish are whale as well.
If we observe the given statements, we can find that in Statement 1 and 2, the middle term ‘shark’ is distributed twice and therefore even after conversing either of the sentence we won’t be able to find a definite conclusion out of these two. Therefore, we can’t derive a definite relationship between ‘deer’ and ‘whale’.
C1 hence doesn’t follow.
Checking C2: No whale is a fish.
Following the logic explained above, we can clearly say that C2 doesn’t follow either.
Checking C3: Some deer are not shark.
From S2 and S3,
Not a single shark is fish (E) + Every fish are deer (A) = Some deer are not shark.
Clearly, C3 follows.
Checking C4: No whale is a deer.
Here, once again we are asked to derive a relationship between ‘whale’ and ‘deer’. Clearly, C4 doesn’t follow.
Among all, only C3 follows. Option A is hence the correct answer.
Question 4:
Statements:
All apples are red.
No red is a mango.
All mangoes are sweet.
Conclusions:
I. All apples being sweet is a possibility.
II. No sweet is an apple..
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 conclusions I and II follow
Solution:
All apples are red (A) + No red is a mango (E) = A + E = E = No apple is a mango, now
No apple is a mango (E) + All mangoes are sweet (A) = E + A = O* = Some sweet are not apples.
Hence, conclusion I follows, but conclusion II does not follow.
Hence, option A is correct.
Question 5:
Statements:
Some rabbits are black.
No black is a tall.
All tall are white.
Conclusions:
I. Some white are not black.
II. All rabbits being tall is a possibility.
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 conclusions I and II follow
Solution:
No black is a tall (E) + All tall are white (A) = E + A = O* = Some white are not black. Hence, conclusion I follows.
Again, Some rabbits are black (I) + No black is a tall (E) = I + E = O = Some rabbits are not tall. Thus, the possibility in II does not exist. Hence, conclusion II does not follow.
Hence, option A is correct.
Question 6:
Statements:
Some questions are answers.
Some answers are explanations.
All explanations are lengthy.
No lengthy is a summary..
Conclusions:
I. No explanation is summary.
II. Some lengthy are answers.
III. Some answers are not summary.
A. Only conclusion I follows
B. Only conclusion II follows
C. Both conclusion I and II are true
D. All conclusions follow
E. None of the above
Solution:
All explanations are lengthy (A) + No lengthy is summary (E) = A + E = No explanation is a summary. Hence, conclusion I follows
Some answers are explanations (I) + All explanations are lengthy (A) = I + A = I = Some answers are lengthy – converse – Some lengthy are answers. Hence conclusion II follows.
Some answers are lengthy (I) + No lengthy is a summary (E) = Some answers are not summary. Hence, conclusion III follows.
So, all the conclusions follow.
Hence, option D is correct..
Question 7:
Statements:
Some stars are planets.
All planets are comets.
No comet is asteroid.
Some asteroids are eclipse..
Conclusions:
I. Some asteroids are stars.
II. Some eclipse being comet is possibility.
III. No asteroid is star.
A. Only conclusion I follows
B. Only conclusion II follows
C. Only conclusions I and III follow
D. Either conclusion I or II follows
E. Either conclusion I or III and conclusion II follow
Solution:
Some stars are planets (I) + All planets are comets (A) = I + A = I = Some stars are comets (I) + No comet is asteroid (E) = I + E = O* = Some stars are not asteroid.
Therefore, conclusion I and III form an I-E type of complementary pair. Therefore, either conclusion I or III follows.
No comet is asteroid – converse – No asteroid is comet; Some asteroid are eclipse – converse – Some eclipse are asteroid
Some eclipse are asteroid (I) + No asteroid is comet (E) = I + E = O* = Some eclipse are not comets. Hence, ‘Some eclipse being comet is possibility’.
Hence, option E is correct..
Question 8:
Statements:
Some companies are industries.
Some industries are primary.
All primary are services.
All services are secondary
Conclusions:
I. All companies being primary is possibility.
II. All services are not primary.
III. No industry is secondary.
A. Only conclusion I follows
B. Only conclusion II follows
C. Only conclusion I and III follow
D. All conclusions follow
E. None of the above
Solution:
Some companies are industries (I) + Some industries are primary (I) = I + I = No conclusion follows but possibility exists because the statement are positive. Hence, conclusion I follows.
As statements II and III are positives therefore, conclusions II and III do not follow.
Hence, option A is correct..
Syllogism Questions for Bank Exams:
Question 1:
Statements:
Only a few Chart are Turbine.
Only a few Turbine are Pores.
Only a few Pores are fan.
Conclusions:
I. Some fan is chart is a possibility.
II. All fan are Turbine.
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 conclusions I and II follow.
Solution:
Checking C1. Some fan is chart is a possibility.
As there is no negative statement, the possibility in C1 does exist. Hence, C1 follows here.
Checking C2 : All fan are Turbine.
When all given statements are 'I' type, a definite conclusion 'All fans are Turbine.' is not possible. Hence, C2 doesn't follow here.
Option A is the right answer.
Question 2:
Statements:
All Beaches are Deltas.
All Deltas are cushions.
No Cushions is wave.
Conclusions:
I. Some Beaches can be wave.
II. No Deltas is Wave.
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 conclusions I and II follow.
Solution:
Checking C1. Some Beaches can be wave.
Using S1 and S2, we get
All Beaches are Deltas (A) + All Deltas are cushions (A) ⇒ All Beaches are cushions.
Now, using the above derived conclusion and S3, we get
All Beaches are cushions + No Cushions is wave ⇒ No beach is wave.
Clearly, C1 doesn't follow.
Checking C2. No Delta is Wave.
Using C2 and C3, we get
All Deltas are cushions + No Cushions is wave ⇒ No delta is wave.
Clearly, C2 follows here.
Hence, option B is the correct answer.
Question 3:
Statements:
Only a few Aces are Club.
No club is Jack.
Only a few Jack are Diamond.
Conclusions:
I. Some Diamond are Aces.
II. Some Aces are Jack.
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 conclusions I and II follow.
Solution:
Checking C1. Some Diamond are Aces.
Using S1 and S2, we get
'Only a few Aces are Club' or 'Some aces are club' + No club is Jack ⇒ Some aces are not jacks.
Using the above derived conclusion and S3, we get
Some aces are not jacks + Only a few Jack are Diamond or 'Some jacks are diamonds' ⇒ No valid conclusion
Clearly, C1 doesn't follow.
Checking C2. Some Aces are Jack.
Using S1 and S2, we get
'Only a few Aces are Club' or 'Some aces are club' + No club is Jack ⇒ Some aces are not jacks.
Clearly, C2 doesn't follow either.
Option D is hence the correct answer.
Question 4:
Statements:
Some Apple are Banana.
No Banana is Date.
Conclusions:
I. Some Date are not Apple is a possibility.
II. All Apple can never be Date.
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 conclusions I and II follow.
Solution:
Statements:
Some Apple are Banana.
No Banana is Date.
Conclusions:
I. Some Date are not Apple is a possibility.
II. All Apple can never be Date.
Checking C1. Some Date are not Apple is a possibility.
Some Apple are Banana (I) + No Banana is Date (E) ⇒ Some apples are not dates.
Here, we are not sure of the elements of the class 'dates' which means 'Some dates are not apples' may be a possiblity.
Hence, C1 follows here.
Checking C2. All Apple can never be Date.
Following the explanation given for C1, we can observe that when 'Some apples are not dates', 'All apples can never be date.' has to be true.
Hence, C2 follows.
Option E is hence the correct answer.
Question 5:
Statements:
All malware are software.
A few software are ransomware.
Most of the pals are ransomware..
Conclusions:
I. All ransomware can be pals.
II. Some malware is an ransomware.
A. Only I follows
B. Only II follows
C. If either I or II follows
D. If neither I nor II follows
E. If both I and II follow
Solution:
Statements:
All malware are software.
A few software are ransomware.
Most of the pals are ransomware.
Conclusions:
I. All ransomware can be pals.
II. Some malware are ransomware.
Checking C1:
As there is no negative statement, possibilities among classes do exist. C1 hence follows.
Checking C2:
All malware are software. + A few software are ransomware. = No definite conclusion because the middle term 'Software' is not distributed even once. C2, hence, doesn't follow.
Option A is hence the correct answer.
Question 6:
Statements:
All hatchbacks are sedans.
No sedan is an SUV.
All SUVs are crossovers.
Conclusions:
I. No crossover is a hatchback.
II. All sedans being crossovers is a possibility.
A. Only I follows
B. Both I and II follow
C. Only II follows
D. Either I or II follows
E. Neither I nor II follows
Solution:
In conclusion II we need to derive a relationship between the classes ‘crossover’ and ‘hatchback’ which are present in S3 and S1 respectively.
By applying the deduction method on S1 and S2, we get ‘No hatchback is a SUV’. Now taking this and S3, we can once again apply the deduction method and get the conclusion as ‘Some crossovers are not hatchbacks’ which is not given as a conclusion. Conclusion I hence doesn’t follow.
For conclusion II, we can take S2 and S3 and apply the deduction method. The derived conclusion is ‘Some crossovers are not sedans’. Here, we are not sure of the elements of the class ‘sedans’ and therefore the possibility ‘All sedans being crossover’ exists. Conclusion II, thus, follows.
Option C is hence the correct answer.
Question 7:
Statements:
All water tanks are houses.
No road is garden.
All houses are temples.
Conclusions:
I. Some temples are water tanks.
II. All temples are houses.
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.
Solution:
Statements:
All water tanks are houses.
No road is gardens.
All houses are temples.
Conclusions:
I. Some temples are water tanks.
II. All temples are houses.
All water tanks are houses (A) + All houses are temples (A) = A + A = A = All water tanks are temples (A) – conversion – Some temples are water tanks. Hence, conclusion I follows.
Again, All houses are temples – conversion – Some temples are houses. Hence, conclusion II does not follow.
Hence, the correct answer is option A.
Question 8:
Statements:
No hen is a cock.
Some ducks are hens.
No cock is a sparrow.
Conclusions:
I. No hen is a sparrow.
II. Some ducks are not cocks.
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
Solution:
No hen is a cock (E) + No cock is a sparrow (E) = E + E = No conclusion. Hence conclusion I does not follow.
Again, Some ducks are hens (I) + No hen is a cock (E) = I + E = I + E = O* = Some ducks are not cocks. Hence conclusion II follows.
Hence, option B is correct.
Syllogism Questions for SSC Exams:
Question 1:
Statements:
All mobiles are laptops.
Some laptops are tablets.
Conclusions:
I. All tablets being mobiles is a possibility.
II. All laptops being tablets is a possibility.
A. If only conclusion I follow
B. If only conclusion II follow
C. If either conclusion I or conclusion II follows
D. If both the conclusions follow
Solution :
There is no negative statement. Thus the possibilities exist in I and II. Hence, both the conclusion I and II follow.
Hence, option D is correct.
Question 2:
Statements:
No paper is a pen.
Some registers are papers.
All copies are pens.
Conclusions:
I. Some papers are registers.
II. No copy is a paper.
A. If only conclusion I follows
B. If only conclusion II follows
C. If either conclusion I or II follows
D. If both conclusion I and II follow
Solution :
Some registers are papers (I) - conversion - Some papers are registers (I). Hence conclusion I follows.
Again, All copies are pens (A) + (No paper is a pen (E) - ) conversion - No pen is a paper = A + E = E = No copy is a paper. Hence conclusion II follows.
Hence option D is the correct answer.
Question 3:
Statements:
I. Some pencils are eraser.
II. No eraser is a bag.
Conclusions:
I. Some eraser are not bags.
II. All eraser are pencils.
III. Some pencils are not bags.
A. Only conclusion 1 follow
B. Only conclusion 1 and 3 follow
C. All Conclusions Follow
D. None of these
Solution :
No erasers is a bag (E) → conversion→ No bag is a eraser.Hence conclusion 1 does not folllow
Some pencils are eraser 1 → conversion → Some eraser are pencils. Hence conclusion does not follow
Some pencils are eraser + No eraser is a bag (E) = I + E = O* = Some pencils are not bags. Hence conclusion 3 follow.
Hence, option D is correct.
Question 4:
Statements:
No bike is a car.
Some trucks are Bikes.
No car is a bus.
Conclusions:
I. No bike is a bus.
II. Some trucks are not cars.
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
Solution:
No bike is a car (E) + No car is a bus (E) = E + E = No conclusion. Hence conclusion I does not follow.
Again, Some trucks are bikes (I) + No bike is a car (E) = I + E = I + E = O* = Some trucks are not cars. Hence conclusion II follows.
Hence, option B is correct.
Question 5:
Statements:
All schools are collages.
Classrooms are schools.
Conclusions:
I. Some Classrooms are collages.
II. Some schools are Classrooms.
A. Only conclusion I follows
B. Only conclusion II follows
C. Either conclusion I or II follows
D. Both conclusions I and II follows
Solution:
Classrooms are schools → All Classrooms are schools (A) + All schools are collages (A) = A + A = A
= All Classrooms are collages → implication → Some Classrooms are collages.
Hence, conclusion I follows.
Again, Classrooms are schools → conversion → Some schools are Classrooms.
Hence conclusion II follows.
Therefore, option (D) is correct.
Question 6:
Statements:
All toys are games.
Some games are stadiums.
Conclusions:
I. All stadiums being toys is a possibility.
II. All games being stadiums is a possibility.
A. If only conclusion I follow
B. If only conclusion II follow
C. If either conclusion I or conclusion II follows
D. If both the conclusions follow
Solution:
There is no negative statement. Thus the possibilities exist in I and II. Hence, both the conclusions I and II follow.
Option D is hence the correct answer.
Question 7:
Statements:
All gurukuls are institutes.
Classes are gurukuls.
Conclusions:
I. Some classes are institutes.
II. Some gurukuls are classes
A. Only conclusion I follows
B. Only conclusion II follows
C. Either conclusion I or II follows
D. Both conclusions I and II follows
Solution:
Classes are gurukuls → All classes are gurukuls (A) + All gurukuls are institutes (A) = A + A = A
= All classes are institutes → implication → Some classes are institutes.
Hence, conclusion I follows.
Again, classes are gurukuls → conversion → Some gurukuls are classes.
Hence conclusion II follows.
Therefore, option (D) is correct.
Question 8:
Statements:
Some printers are scanners.
Some scanners are microphones.
Many microphones are speakers.
Conclusions:
I. Some printers are speakers.
II. Not a single printer is speaker.
A. If only conclusion I follows
B. If only conclusion II follows
C. If either conclusion I or conclusion II follows.
D. If both the conclusions follow
Solution:
Checking Conclusion I and II together : 'Some printers are speakers' and 'Not a single printer is speaker'
Clearly, all the statements are I type, we can't define a relationship between classes scanner exist in two different statements.
Similarly, we can't define a relationship between the classes 'printer' and 'speaker' either.
But, C1 is an I type statement and C2 an E type, and they together form an E+I combination (Complementary Pair).
Clearly, either C1 or C2 follows.
Hence option C is the correct answer.