Syllogisms

How to solve Syllogisms Questions easily in Reasoning Section

The Reasoning section of every competitive exam includes questions from the topic “Syllogisms”. This topic is considered to be quiet important and every year a good number of questions are asked from this topic. It is considered to be a very scoring topic. We are providing you with all the important tools to solve Syllogisms questions easily and accurately.

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.

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 – Means the whole circle representing A lies within the circle representing B.

Here we can also make conclusion: Some B are A. Some A are 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 bat.

No door is wall.

Category 3

Some A are B

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 are B also indicates that – All A are B.

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

(iv) Some A are 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

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 same as some statement.

For ex:

Statement: All kids are innocent.

Here we can make 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 being 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 conclusion: Some pens are not pencils, which is true. In above figure, green shaded part shows; some pens are not pencils, because in 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 conclusion is true and 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.

Conclusion is false because possibility figure is not possible.

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

Important Rule:

Restatement is not a conclusion – Conclusion has to be different from the statement.

E.g.

Statement - All A are B

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

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

Note: If statement and conclusion is same then, conclusion does not follow. This rules also follows in possibilities case.