The Eulerâ€™s Circles or Venn Diagrams
There is a pictorial way of representing the propositions, formulated by Euler, an ancient mathematician. Suppose that the proposition is trying to relate the subject (S) with the predicate (P). Then, there are four ways in which the relation could be made according to the four propositions.
 Diagrammatic representation of â€˜Aâ€™ proposition.
 Diagrammatic representation of â€˜Eâ€™ proposition.
 Diagrammatic representation of â€˜Iâ€™ proposition.
 Diagrammatic representation of â€˜Oâ€™ proposition.
Based on the above analysis, we can tabulate the concepts as in the following table.
If the Type of the Given Proposition is

Then its Diagrammatic Representation is

â€˜Aâ€™
All S are P. 
Always

â€˜Eâ€™
No S are P. 
Always

â€˜Iâ€™
Some S are P.

Either Some S are P.
(Some S are not P.)

or, Some S are P.
(All S are P.)


or, Some S are P.
(All P are S.)


â€˜Oâ€™
Some S are not P.

Either
Some S are not P.
(Some S are P.)

or, Some S are not P.
(All P are S.)


or, Some S are not P.
(No S are P.)
