Syllogism – Basic Rules and Concepts

Syllogism – Basic Rules and Concepts

 

Hello Readers

Today we will discuss Syllogism – Basic Rules and Concepts

Syllogism is one of the important topics of Reasoning, as it generally comes for 5 marks or more. Syllogism is considered as complex topic but, if we will follow the right concepts and techniques, then it’s not difficult to solve these questions.

In Syllogism, there are different statements and conclusions given in the questions. We always consider that given statements are true and then we check which of the given conclusions follow the given statements.

 

Before discussing the examples, let’s understand some important terms related to Syllogism:

 

1) Statement – It is generally given in the question and we always consider it true, even if it is not according to the commonly known facts.

 

2) Conclusion – It is the statement which is derived from the given Statement. Conclusion must be true and follow the statement in every possible case.

 

3) Possibility – It is the statement which is not definitely true. It may be true for some cases but not for all the cases.

 

There are two types of questions that are asked in the examinations – Conclusion Based and Possibility based.

 

Now, we will discuss how these questions come in the examinations and which are the quantifiers used in the questions.

 

Example –

 

Statements –

All A are B

All B are C

Conclusions –

Some C are B

No A is a C

 

As we can see there are different quantifiers used in the above statements and conclusions.

 

Quantifiers – All, Some, No, Every, Each, Few, None etc.

 

Quantifiers can be divided into two types –

 

Universal –Used to cover all the aspects or cases or we can say in which we will consider the total quantity i.e. 100% like All, Each, Every, No

 

Particular – Used to cover a specific or particular quantity or we can say in which they do not cover the total quantity like Some, Few etc.

 

From the above discussed Quantifiers, Some is the most confusing Quantifier while we solve questions of the Syllogism.

 

So let’s discuss few things related to this quantifier.

In general terms, we can say Some is a part.

In Syllogism, we take

Some ranges from Minimum ‘1’ to Maximum ‘100’

 

Example – Some Cats are Bats.

Conclusion –

We can say Some cats are bats even if there will be 1 cat or 10 cats or 50 cats or 100 cats (consider 100 as total)

So from above, we can say that if there will be conclusion –

All Cats are Bats.

Then, it will also be considered as true.

 

Syllogism 1

 

Now, let’s discuss about different types of Statements that are used in Syllogism –

 

Statements –

 

1) All A’s are B’s

 

syllogism statement 1

 

Conclusion – Some B’s are A’s

 

2) No A is B

 

syllogism statement 2

 

Conclusion –No B is A

 

3) Some A’s are B’s

 

syllogism statement 3

 

Conclusion – Some B’s are A’s

 

4) Some A’s are not B’s

 

syllogism statement 4

 

Conclusion – No Conclusion

 

 

Complementary Pair –

Complementary pair is the pair of two such components which are negative of each other.

 

1) No A is B       Some A’s are B’s

 

Complemetary 1

 

2) All A’s are B’s    ⇔   Some A’s are not B’s

 

Complemetary 2

 

So, in complementary pair only one conclusion can be true at same time i.e. either of the given conclusions.

With this we will finish with Basic Concepts of Syllogism. We will discuss few examples in the next article.

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