Introduction

The meaning of syllogism as given by Greeks is Deduction. It’s a kind of logical argumentation.

How to solve Syllogisms?

First, we will know basics of syllogism, How the Venn Diagram can be drawn for both Definite and Possibility cases? You must go through it in detail. Merit shine has already conducted two video sessions on this topic. You can see the video sessions from the link given at the end of this article.

Nowadays, Syllogism are asked in a different way rather than the conventional way. In this new pattern, Conclusions are given and Statement are asked. To study Reverse Syllogism notes you can check the link provided at the end of this article.

Affirmative (+) Negative (-)

Universal All A are B No A are B

Particular Some A are B Some A are not B

Introduction: - The word 'Syllogism' literally means 'logic'. This topic is an important topic of logical reasoning and therefore, knowledge of working rules is necessary to solve the problems.About 5 questions in Banking and IBPS examinations are asked about this topic, so this topic is important.

These questions basically follow nature:

Two or more statements are given in it and it is necessary to know all the possible reasons given in the statement.

Syllogism is an extremely important topic of logical reasoning. Originally in competitive examinations 5-6 questions are asked in this subject and the wen-diagram is used to solve them.

Case I: Universal Affirmative

All A are B

Set A is a subset of B

Can’t infer that “Some B are not A”

It is different from “All B are A”.

Case II: Universal negative

No A are B

Two sets, A and B do not overlap each other in this case.

It is same as “No B are A”.

It can be also written as “All A are not B” and “ All B are not A”.

Case III: Particular Affirmative

Some A are B

There is at least one element that is both in set A and B.

Can’t infer that “Some A are not B”.

It is the same as “Some B are A”.

Case IV: Particular Negative

Some A are not B

There is at least one element in set A that is not a part of set B.

Can’t infer that “Some A are B’.

It is different from “Some B are not A”.

note:- 1. Always accept the statement as true even if it appears different from the known truth.This is the basic concept of syllogism.

2. You should understand the statement correctly, then try to understand its conclusions.

In this type there are two types of conclusions, one is the definite conclusion and another one is the possible conclusion.

Statement type

Type 1

All books are pen

Type 2

There is no book pen

Type 3

Some books are pen

Type 4

There are no books pen

Types of conclusions

Type 1

All books are pen

Type 2

There is no book pen

Type 3

Some books are pen

Type 4

There are no books pen

Type 5

All books are likely to be pen

Type 6

Not all books are likely to be pen

Type 7

Some books may be pen

Syllogism has three parts: - (i) Positive (100%)

(II) Negative (0%)

(III) Chance [(50-50%) (May be or not)]

Positive part (100%)

Examples: - All and some

Statement: - All books are pen

All pen copy

Conclusion: -

All book copy is - √

All pen copy is - √

Some books have pen - √

Some pen book is - √

There is some copy pen - √

Some book is copy - √

All pen books are - X

All Copy Pen is - X

All copy books are - X

II. Negative Part (0%)

Example: - There is no book pen

Statement: - All books are pen

No pen copy

Conclusion: - There is no book copy

No copy pen

Note: - If I relate to book and copy, then no one follows my statement and always focuses on work and omniscient truth in syllogism.

III. Prospect part (50-50%)

Example: - There is a possibility of some common apples

Statement: - All apples are common

Some common oranges

Conclusion: - All of us are likely to have apple - √

Some oranges are not likely to have apples - √

All apples are likely to be common - X

Some oranges are likely to have apples - √

Note: - If there is no direct connection then there may be a possibility , but in some ways my statement should not be wrong.

* Complementary pair: (Ether based)

(a) No boy is a student

(b) Some boys are students

Note: - Nothing statement (unlike all)

Statement: - Some apple oranges are

No orange is not common

Conclusion: - Some apples are not common - X

There are some common oranges - √

Not a few common apples - √

Now, let's understand this from examples:

Statements:

(1)Some Cakes are Roses (2)All Roses are Trucks

(3)No Trucks are Bricks (4)At least some Bricks are Hotels

Conclusions:

(1)Some Trucks are Cakes

(2)Some Bricks are Roses

(3)All Cakes are Trucks

(4)Some Hotels are Cakes

Solution: First, you should draw basic diagrams

Now, we can see that

Conclusion1 is true. As Cakes and Trucks are intersecting each other.

Conclusion2: There is no relation mentioned between Bricks and Roses. So, we can’t comment about it.

Conclusion3: Intersection of Trucks and Cakes is due to Roses. We can’t comment about all Cakes.

Conclusion4: There is no relation mentioned between Hotels and Cars. So, we can’t comment about it.

Hence, Conclusion 1 follows.

Possibility Cases

In the case of Possibility cases, we have to infer all possible cases which can be possible. In exams, you don’t need to draw diagram for each and every possible case. In this, the basic and definite condition should not be changed.

Solve reverse syllogism?

To solve Reverse Syllogisms through

Elimination method

In this method, we try to eliminate the options step by a step which cannot be answer. Steps should be taken in eliminating the options are given below.

First, always identify “Universal Negative” conclusion, then eliminate those options which do not have a single universal negative statement.

Secondly, check “Particular Negative” conclusion, then eliminate those options which violates this condition.

Thirdly, check “Universal Positive” conclusion, then eliminate the option which also violate this condition.

In last, check “Particular positive” conclusion, then eliminate the option which also violate this condition.

In last the remaining option will be your answer.

Let's discuss

with examples.

Example 1

Conclusion:

(1) No toxic is injection. (2) Some injections are glucose.

Statements:

(A) All toxic are tablet. No tablet is glucose. Some glucose are medicine. All medicine are injection.

(B) Some toxic are tablet. All tablet are injection. Some injection are glucose. All glucose are medicine.

(C) All tablet are toxic. No injection is toxic. Some glucose are injection. All glucose are medicine.

(D) Some injection are toxic. All injection are tablet. Some toxic are glucose. All glucose are medicine.

(E) Some medicine are toxic. Some toxic are injection. Some injection are tablet. All tablet are glucose.

Solution:

In Reverse Syllogism, Conc.1is Universal negative or disjointed set. So first we will try to find out the option which has the statement following this conclusion.

We can see that, In option B, D and E, there is no negative statement. So these cannot be answer.

In option A and C, there is negative statement. In option C, you can see the statement 2 and statement 3 depict the given conclusion.So, C is the answer.

You can also check option A, but when you have got your answer, there is no use of wasting time.

Now, Question is why I checked first option C?

I checked both option A and C, but in C I found related information to Conclusion, So, I go in detail of it.

syllogism with example

Q 1 - Statements:

I. Some pigs are bachelors.

II. All bachelors are blessed.

Conclusions:

I. Some pigs are blessed.

II. At least some blessed are bachelors.

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 follows.

Answer : E

Explanation

Some pigs are bachelors (I) + all bachelors are blessed (A) = I + A = I = some pigs are blessed. Hence conclusion I follows. Again all bachelors are blessed - conversion - some blessed are bachelors. Hence conclusion II also follows.

Q 2 - Statements:

I. Some pictures are beds.

II. All beds are trees.

Conclusions:

I. Some pictures are trees.

II. At least some trees are beds.

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 follows.

Answer : E

Explanation

Some pictures are beds (I) + all beds are trees (A) = I + A = I = some pictures are trees. Hence conclusion I follows. Again all beds are trees - conversion - some trees are beds. Hence conclusion II also follows.

Q 3 - Statements:

I. Some ninjas are dogs.

II. No dogs is a liar.

Conclusions:

I. No ninja is a liar.

II. At least some ninjas are liars.

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 follows.

Answer : C

Explanation

Some ninjas are dogs (I) + no dog is a liar (E) = I + E = O = some ninjas are not liars. But conclusion I and II make a complementary pair (I - E). Hence either I or II follows. So option C is correct.

Q 4 - Statements:

I. Some necklace are diagrams.

II. No diagram is a lollipop.

Conclusions:

I. No necklace is a lollipop.

II. At least some necklaces are letters.

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 follows.

Answer : C

Explanation

Some necklaces are diagrams (I) + no diagram is a lollipop (E) = I + E = O = some necklace are not lollipop. But conclusion I and II make a complementary pair (I - E). Hence either I or II follows. So option C.

Q 5 - Statements:

I. Some mangos are brinjals.

II. Some carrots are brinjals.

Conclusions:

I. All mangos are carrots.

II. At least some brinjals are not carrots.

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 follows.

Answer : D

Explanation

Some mangos are brinjals (I) + (some carrots are brinjals (I) - conversion -) some brinjals are carrots (I) = I + I = no conclusion. Hence conclusion I and II do not follow.

Q 6 - Statements:

I. Some rifles are bombs.

II. Some cigars are bombs.

Conclusions:

I. All rifles are cigars.

II. At least some bombs are not cigars.

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 follows.

Answer : D

Explanation

Some rifles are bombs (I) + (some cigars are bombs (I) - conversion -) some bombs are cigars (I) = I + I = no conclusion. Hence conclusion I and II do not follow.

Q 7 - Statements:

I. No cake is a ginger.

II. Some gingers are garlic.

Conclusions:

I. No cake is a garlic.

II. Some garlics are not cakes.

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 follows.

Answer : B

Explanation

No cake is a ginger (E) + some gingers are garlics (I) = E + I = O ∗ = some garlics are not cakes. Hence conclusion II only follows, but I does not follow.

Q 8 - Statements:

I. No cash is a flash.

II. Some flashes are bears.

Conclusions:

I. No cash is a bear.

II. Some bears are not cash.

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 follows.

Answer : B

Explanation

No cash is a flash (E) + some flashes are bears (I) = E + I = O ∗ = some bears are not cash. Hence conclusion II only follows, but conclusion I does not follow.

Q 9 - Statements:

I. No pizza is a burger.

II. No chautney is a burger.

Conclusions:

I. Some pizzas are not chautneys.

II. Some burgers are chautneys.

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 or II follows.

E - If both conclusion I and II follows.

Answer : D

Explanation

No pizza is a burger (E) + (no chautney is burger-conversion -) no burger is a chautney (E) = E + E = no conclusion. Hence conclusion I does not follow. Again, no chautney is a burger - conversion - no burger is a chautney. Hence conclusion II also does not follow.

Q 10 - Statements:

I. All fingers are levers.

II. Some levers are fringe.

Conclusions:

I. Some fringe are levers.

II. No fingers is a fringe.

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 or II follows.

E - If both conclusion I and II follows.

Answer : A

Explanation

All fingers are levers (A) + some levers are fringe (I) = A + I = no conclusion. Hence conclusion II does not follow. Again, some levers are fringe (I) - conversion - some fringe are levers (I). Hence conclusion I follows.