Formulas for Syllogism

Formulas for Syllogism and Definition

Syllogism is one of the most frequently asked questions in the competitive exams. Formulas for Syllogism is given here on this page.

Such type of questions contains two or more statements which may or may not have any connection with reality. Two or more conclusions follow these statements.

Now we have to find out which conclusion is somewhat similar or follow the given statement.

Here you will learn new way to solve syllogisms problem with given rules.

Formulas for Syllogism

Syllogism Formulas To Solve Problems:

  • Some + All= Some
  • Some + Some= No Conclusion
  • Some + No= Some Not
  • No + No= No Conclusion
  • No +All = Some Not Reversed
  • No + Some = Some Not ( Reversed )
  • Some Not/ Some Not Reversed + Anything= No Conclusion
  • No + All = Some not Reversed
  • All + Some = No Conclusion
  • All + All= All
  • All + No= No

Formulas for Syllogism and Concept:

Note: For understanding the syllogism formulas it is important to understand below 4 points. Before stating further.

S.NoType of statementRepresented by the letter
1.Universal PositiveA
2.Universal NegativeE
3.Particular PositiveI
4.Particular NegativeO

Universal Positive Statement:

Universal positive statement indicates something positive applicable to all the items in that category. This is represented by the letter ‘A’. These statement begin with All, Every and Even.

Universal Negative Statement:

It implies that it refers to that kind of statements, which are universal and giving a negative impression. These types of statements begin with No, None of the, Not a single etc. and are represented by the letter ‘E’

Particular Positive Statement:

These type of statements begins with some, any, a few and are represented by the letter ‘I’.

Particular Negative Statement:

These kinds of statements are represented by the letter ‘O’. Some examples of this are:

  • Some girls are not crazy
  • Some files are not pencils
  • Some M is not N
  • Some Rohits are not Dhawans.
  • Few vegetables are not green.

Since there is no specific formula for solving such type of questions, but it is suggested to take the help of Venn Diagrams.

All we have to do is, read the given statements and accordingly draw the Diagram step by step, on the basis of the given statements, and eventually derive a logical solution by these diagrams.

Question 1.

To give an elite education to their children, parents today are ready to pay any amount.

I.  All parents are very rich these days
II. Parents are obsessed for perfect development of their children.

A. Only conclusion I follows
B. Only conclusion II follows
C. Either I or II follows
D.Neither I nor II follows
E. Both I and II follows

Correct Answer: B


The statement points that people are motivated towards providing their children an elite education. All parents are rich or not, it is not mentioned in the statement. Hence, only conclusion II follows and I does not.

Question 2.


The average number of persons educated per family is 2 in urban areas whereas it is 1 in rural areas.


I. The literacy rate in the rural areas is lower than in the urban areas.

II. Fewer people are educated in the rural areas as compared to those in urban areas.

Correct Answer: E


Clearly both the statements can be induced from the statement. Hence both I and II follows

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