The word ‘Syllogism’ is also referred to ‘Logic’. Syllogism is an important section of logical reasoning and hence, a working knowledge of its rules is required to solve the problems. In banking and IBPS exams they ask 5 questions on this hence it is an important topic for Banking exams.
It can be expressed as the ‘Science of thought as expressed in language’. The questions based on syllogism can be solved by using Venn diagrams and some rules devised with the help of analytical ability
These questions are usually of the following nature:
Two or more statements are given and one is supposed to find out all the possible conclusions from the given statements. Lets take the example of two statements:
All A’s are B’s All B’s are C’s
Now a conclusion has to be found out using these two statements together. There are two popular methods of solving Deduction based questions:
1. Theory of Venn Diagram – Diagram based
2. Theory of Syllogism – Rules based
The method of Syllogism is preferable when a conclusion has to be derived using two statements only. For these types of questions,
Venn-Diagram method is time consuming. But if the number of statements are more than two then, Syllogism method is time consuming, hence the Venn Diagram method should be used.
Terms to know:
1. Premise, Conclusion
2. Number of terms
3. Subject & Object
4. Quantifier – Types
5. Middle Term (common term in the two statements)
Types of Quantifiers:
1. Universal Affirmative: All, Any, Each, Every
2. Universal Negative: No, Not
3. Particular Affirmative: Some, Few, Many, Little, Most, Much, Several, etc
4. Particular Negative: Some Not, Few not, Many not, Most not, Much not, Several not, All not, Not all, etc
It is also referred to as ‘Premises’. It is a sentence which asserts that either a part of, or the whole of, one sets of objects-the set identified by the subject term in the sentence expressing that sentence either is included in, or is excluded from, another set-the set identified by the predicate term in that sentence.
Types of Proposition
Categorical Proposition There is relationship between the subject and the predicate without any condition.
Example : I. All beams are logs.
II. No rod is stick.
Hypothetical Proposition: There is relationship between subject and predicate which is asserted conditionally.
Example : I. If it rains he will not come.
II. If he comes, I will accompany him.
Disjunctive Proposition In a disjunctive proposition the assertion is of alteration.
Example : I. Either he is brave or he is strong.
II. Either he is happy or he cannot take revenge.
Parts of Proposition It consists of four parts.
1.Quantifier: In quantifier the words, ‘all’, ‘no’ and ‘some’ are used as they express quantity. ‘All’ and ‘no’ are universal quantifiers because they refer to every object in a certain set. And quantifier ‘some’ is a particular quantifier because it refers to at least one existing object in a certain set.
2.Subject: It is the word about which something is said.
3.Predicate: It is the part of proposition which denotes which is affirmed or denied about the subject.
4.Copula: It is the part of proposition which denotes the relation between the subject and predicate.
1. Any two premises should contain three and only three distinct terms.
2. If any one of the two premises is particular, then the conclusion, if any, must be particular.
3. If any one of the two premises is negative, then the conclusion, if any, must be negative.
4. If both the premises are particular no conclusion is possible.
5. If both the premises are negative no conclusion is possible.
6. To obtain the conclusion, the middle term, must be distributed at least once, in the two premises.
7. Any term that has not been distributed in the premises, cannot be distributed in the conclusion.
Rules 1 to 5 can be combined to make a combination table:
Types of Questions Asked in the Examination
There are mainly two types of questions which may be asked under this 1. When premises are in specified form Here premise is in specified form. Here mainly two propositions are given. Propositions may be particular to universal; universal to particular; particular to particular; universal to universal
2.When premises are in jumbled/mixed form Here at least three or more than three proposition are given. Here pair of two propositions out of them follow as same as in specified form.
Type 1 Premises in Specified Forms
Case 1: The conclusion does not contain the middle term Middle term is the term common to both the premises and is denoted by M. Hence, for such case, conclusion does not contain any common term belong to both premises
Example 1 Statement:
I. All men are girls. II. Some girls are students.
Conclusions I. All girls are men. II. Some girls are not students.
Solution. Since, both the conclusions I and II contain the middle term ‘girls’ so neither of them can follow.
By using both representation (a) and (b) it is clear all girls cannot be men as well as (a) shows some girls are students, here no man is included but at the same time (b) shows some girls are students have some men are also students as all men are girls. Hence, we cannot deduce conclusion II.
So, neither of them can follow.
Statement: I. All mangoes are chairs.
II. Some chairs are tables.
Conclusions I. All mangoes are tables.
II. Some tables are mangoes.
III. No mango is a table.
Solution. Here, the term chair is common to both the statement and hence, is the middle term. Statement (I) is A type proposition and in A-type proposition, only subject is distributed, hence, chair being the predicate in the statement (I) is not distributed in the second statement. Thus, none of the conclusions following statement is a valid inference.
Venn diagram representation: All possible cases can be drawn as
(i)All mangoes are table-this inference is definitely false neither (a) nor (b) shows this conclusion.
(ii)Some tables are mangoes, this inference is uncertain or doubtful.
(iii) No mango is a table, this inference is also uncertain or doubtful. Though it can be concluded from the above discussion that no valid inference can be drawn between mango and table.
Case 2: No term can be distributed in the conclusion unless it is distributed in the premises.
If case 1 is compiled with by a pair of statement, it is confirmed that valid mediate inferences can be drawn from such pair of statement. But every mediate inference drawn cannot be valid. Therefore, case 2 is applied to check as to the conclusions drawn from a pair of statement in which middle term is distributed, is valid.
Statement: I. Some boys are students. II. All students are teenagers.
Conclusions I. All teenagers are students. II. Some boys are teenagers.
Solution. Statement I is an I-type proposition which distributes neither the subject nor the predicate. Statement II is an A type proposition which distributes the subject ‘students’. Conclusion I is an A-type proposition which distributes the subject ‘teenagers’ only. Since. the term teenagers is distributed in conclusion I without being distributed in the premises. So, conclusion I cannot follow. In second conclusion, where it is asked that some boys are teenagers. But from statement I it is clear that some students are not students. These students may not be teenagers.
Venn diagram representation: All possible cases can be drawn as follows
We have given that all students are teenagers so, its reverse cannot be possible. Hence, conclusion I is false. As we are also given that some boys are students and all students are teenagers. So, some boys which are students must be teenagers. Hence, conclusion II follows.
Case 3: If one premises is particular, conclusion is particular. Take an example which explains this case
Statement: I. Some boys are thieves.
II. All thieves are dacoits.
Conclusions I. Some boys are dacoits.
II. All dacoits are boys.
Solution. Since, one premise is particular, the conclusion must be particular. So, conclusion II cannot follow.
Venn diagram representation: All possible cases can be drawn as follows
Here conclusion I follows but the conclusion II cannot follow.
Case 4 If the middle term is distributed twice, the conclusion cannot be universal Take an example which explains such case.
Example 5 Statement: I. All Lotus are flowers. II. No Lily is a Lotus.
Conclusions I. No Lily is flowers. II. Some Lilies are flowers.
Solution. Here, the first premise is an A proposition and so, the middle term ‘Lotus’ forming the subject is distributed.The second premise is an E proposition and so, the middle term ‘Lotus’ forming the predicate is distributed. Since, the middle term is distributed twice, so the conclusion cannot be universal.
Venn-diagram representation: All possible cases can be drawn as follows
It is clear from the given Venn-diagrams either conclusion I or II must be followed.
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