Logical Venn Diagrams
Logical Venn diagrams represent the logical relationship among different items. The items are represented by circles or any other geometrical figures. The size and shape of the diagrams have no relevance to the quantity or nature of the items they represent. They represent only the logical relation among the items.
To start with, we shall analyse as to how the relation between two items can be represented by way of logical Venn diagrams.
There can be only three types of relationships between any two different items. The diagrammatic representation of such relationships is given below:
To start with, we shall analyse as to how the relation between two items can be represented by way of logical Venn diagrams.
There can be only three types of relationships between any two different items. The diagrammatic representation of such relationships is given below:
1.  This diagram indicates that one item is completely contained in the other item, but not viceversa.


2.  This diagram indicates that neither item is completely contained in the other item, but the two items have some portion in common.


3.  This diagram indicates that nothing is common between the two items represented by the circles.

The logical relation among the three items can be represented by any one of the following Venn diagrams.
Normally, in the problems on Venn diagrams, a set of Venn diagrams are given followed by a set of three items each. Students are required to choose the appropriate diagram which illustrates the relationship among the three given items. All 11 types of representations are discussed in this chapter by taking an example of each type.