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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:
1. Description: 49083.png This diagram indicates that one item is completely contained in the other item, but not vice-versa.
Example: Fruits, Mangoes. Fruits are represented by the outer circle and Mangoes are represented by the inner circle.
2. Description: 49093.png This diagram indicates that neither item is completely contained in the other item, but the two items have some portion in common.
Example: Teachers, Poets. Some teachers may be poets, but all the teachers are not poets. Similarly, some but not all poets may be teachers. The common portion in both the circles represents the teachers who are also poets.
3. Description: 49102.png This diagram indicates that nothing is common between the two items represented by the circles.
Example: Boys, Girls. Since the two items are entirely different from each other, the circles representing the items do not intersect.

The logical relation among the three items can be represented by any one of the following Venn diagrams.
Description: 49111.png
Description: 49119.png
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.

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