The idea of representing classes and their relation expressed in a proposition by use of circles was originally developed by Euler, a Swiss mathematician of eighteenth century. But its subsequent development and refinements are due to Venn, a British logician belonging to nineteenth century.
The procedure for representing categorical proposition by Venn diagrams is fairly simple and straight forward. We have noted that a categorical proposition consists of two terms as it expresses a relation of inclusion or exclusion between the classes delineated by these two term- In Venn diagram a term is represented by a circle. The area inside the circle represents its denotation. Thus all the members of the class designated by the term would be located within the circle and everything else would be located outside the circle. We shall draw the circles inside a rectangle which would represent the world or the domain of our discourse. The symbol ‘V’ stands for domain of discourse.
In Venn diagram we try to show whether a class or a region inside the domain of discourse is empty or non-empty. To show that a class term has no members or that it is empty, we shade the circle that represents the term. If a class has at least one member than the class is the non-empty. We represent this by putting ‘X’ mark inside the circle.
For example, to say that the class A is empty we draw a circle and then represent the emptiness of A by shading the whole of A as give- below in the figure I. Shading an area means that the area contains nothing. It can be expressed symbolically as “A = O.” (A is equal to zero).