The Reasoning section of teaching exams like KVS, DSSSB and others includes questions from the topic “Syllogisms”. The syllogism is very important not only for DSSSB but for all the teaching exams. Students generally find difficulty in understanding Syllogism. In this article, we have explained the basics of a syllogism with the help of the Venn diagram. Sit with pen and paper while going through this article.
Syllogism Concepts for Teaching Exams
Syllogism comes under the verbal reasoning section and is frequently asked in many competitive exams. These types of questions contain two or more statements and these statements are followed by the 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.
All A are B – 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 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.
No A is B – means that circles representing A and B does not intersect at all.
For example, No ball is the bat.
No door is a wall.
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.
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.
|Types of Sentences||Conclusions|
|All A are B||Some B's are A|
|Some A's are B|
|Some A are B||All A are B|
|All B are A|
|Some B are A|
|Some A are not B|
|No A is B||No B is A|
|Some A are not B||Some A are B|
|All B are A|
|No A is B|
Important Points –
1. At least statement – At least statement is same as some statement.
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 being true then Some not being false
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, green-shaded part shows; some pens are not pencils, because in a statement it is already given No pencils is 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 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 a 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.
Statement: All A are B. Some B are C.
Conclusion: All A being C is a possibility.
The conclusion is true.
Possibility figure –
Statements: No stone is a white. Some white are papers.
Conclusions: I. All stones being paper is a possibility.
Conclusion is true.
Statements: Some mouse is cat.
All mouse are pets. No pet is animal.
Conclusions: I. All mouse being an 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 animal and All mouse is pet. So we can make also conclusion here that no mouse are animal is true.
The statement itself 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 the statement and conclusion are same then the conclusion does not follow. This rules also follow in possibilities case.
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