# How to solve Syllogisms Questions easily in Reasoning Section

By Ashish Kumar|Updated : January 16th, 2022

### Syllogism

Syllogism is a verbal reasoning type problem, which is an important topic and is frequently asked in many competitive examinations in the Reasoning Section. These types of questions contain two or more statement and these statements are followed by the number of conclusion. You have to find which conclusions logically follows from the given statements.

### Syllogism

Syllogism is a verbal reasoning type problem, which is an important topic and is frequently asked in many competitive examinations in the Reasoning Section. These types of questions contain two or more statements and these statements are followed by a number of conclusions. You have to find which conclusions logically follows from the given statements.

The best method of solving the Syllogism’s problem is through Venn Diagrams. There are four ways in which the relationship could be made.

Category 1

All A are B – This means the whole circle representing A lies within the circle representing B.

Here we can also make a conclusion: Some B is A. Some A is B.

For example, All boys are men.

Here we can also make a conclusion: Some men are boys. Some boys are men.

All apples are fruits.

Here we can also make a conclusion: Some fruits are apples. Some apples are fruits.

Category 2

No A is B – means that circles representing A and B does not intersect at all.

For example, No ball is a bat.

No door is the wall.

Category 3

Some A are B

This means that some part of the circle represented by A is within the circle represented by B.

This type of (category 3) statement gives the following conclusions:

(i) Some A are B also indicates that - Some A are not B

(ii) Some A is B also indicates that – All A are B.

(iii) Some A is B also indicates that – All B are A.

(iv) Some A is B also indicates that – All A are B and All B are A.

For e.g.: Some mobiles are phones.

(i)

Category 4.

Some A are not B

This means that some portion of circle A has no intersection with circle B while the remaining portion of circle A is uncertain whether this portion touches B or not.

(i) Some A are not B also indicates that – Some A are B.

(ii) Some A are not B also indicates that – No A is B.

Important Points –

1. At least statement – At least statement is the same as some statement.

For  ex:

Statement: All kids are innocent.

Here we can make a conclusion: At least some innocent are kids (Some innocent are kids).

2. Some not statement: Some not statement is opposite to “All type” statement. If All is true then Some not being false

For e.g.

1. Statement: Some pens are pencils. No pencils are jug. Some jug is pens.

Here we can make a conclusion: Some pens are not pencils, which is true. In the above figure, the green-shaded part shows; some pens are not pencils, because in the statement it is already given No pencils are jug.

Complementary Pairs: (Either & or) – Either and or cases only takes place in complementary pairs.

Conclusions: (i) Some A are B.            (ii) No A are B.

From the given above conclusions, it is easy to understand that one of the given conclusions must be true, which is represented by option either (i) or (ii). These types of pairs are called complementary pairs.

Note: ‘All A are B’ & ‘Some A are not B’ are also complementary pairs.

Note: It is important to note that, in complementary pairs, one of the two conclusions is true and the other will be false simultaneously.

For example –

Statement: All A are B. Some B are C.

Conclusion: I. All C are A. II. Some C are not A.

Here we can make conclusion, either I or either II follows.

Possibility cases in Syllogism – In possibilities cases, we have to create all possibilities to find whether the given conclusion is possible or not. If it is possible and satisfies the given statement than given conclusion will follow otherwise conclusion will not follow.

1. E.g.

Statement: All A are B. Some B are C.

Conclusion: All A being C is a possibility.

Conclusion is true.

Possibility figure –

2. E.g.

Statements: No stone is a white.  Some white are papers.

Conclusions: I. All stones being paper is a possibility.

Possibility figure:

Conclusion is true.

3. E.g.

Statements: Some mouse is cat.

All mouse are pets.  No pet is animal.

Conclusions: I. All mouse being animal is a possibility.

The conclusion is false because the possibility figure is not possible.

If we say all mouse being an animal is a possibility is true then given statements No pet is the animal will be wrong. Here in the statement, it is given No pet is an animal and All mouse is a pet. So we can make also the conclusion here that no mouse is an animal is true.

Important Rule:

The restatement is not a conclusion – The conclusion has to be different from the statement.

E.g.

Statement - All A is B

Conclusion - All are B. (invalid) Conclusion does not follow.

Conclusion - Some A are B (follow) Conclusion follows.

Note: If the statement and conclusion are the same then, the conclusion does not follow. This rule also follows in the possibilities case.

Thanks!

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