## Logical Venn Diagram

The questions relating to logical Venn diagrams test the candidates’ ability to relate and comprehend a certain groups of items and illustrate it diagrammatically. You are required to determine whether the items will form sets and their sub-sets if related or are unrelated and will form different sets. The items may be related through intersection or union of sets. Although the language and symbol of yet theory are never used in this type of questions, if you have studied set theory you may find questions on Venn diagram relatively easier.

Suppose you are given three item - A, B and C. Here, it should be noted that each item represents a certain class. Thus, the questions on Venn diagrams are based on the concept of class. A class is a homogeneous group of objects, or entities, i.e., all entities contained in a certain clas have something common among themselves. For example, the class of “human being” includes only humans and not other living beings. When we say “animal” or “animals kingdom”, then we are referring to all types of animals including of course, human beings. Similarly, if we say “living beings”, then we do mean both flora and fauna.

If we are given three items, namely A, B and C, we have be examine only six types of relationship which possibly exist among themselves:

Six Types of Relationships

(i) Relation of A with B.

(ii) Relation of B with C.

(iii) Relation of A with C.

(iv) Relation of B with A.

(v) Relation of C with B.

(vi) Relation of C with A.

Another type of venn-diagrams also appears frequently in SSC examinations. In this type of venn-diagrams a combination of threeor more different geometrical figures, viz. circle, square, rectangle and triangle, is provided, viz. circle, square, rectangle and triangle, is provided. Each geometrical figure in the diagram represents a certain class. The candidates is required to study and analyse the given diagram carefully and then answer the questions that follow.

Now consider the following examples:

**Ex**. On the basis of following diagram in which three rectangles are interlocked answer the questions given below:

Each rectangle represents a certain section of population. Different regions of the diagram are marked a to g. Read the statements of the questions and identify the appropriate region in the diagram.

(i) College students who are Artists but not Singers are represented by which region?

(ii) Which region represents college students who are Artists as well as singers? **Answer: ** (i) College students who are Artists but not singers are represented by region ‘b’.

(ii) College students who are Artists as well as singers can be represented by the region which is common to all three circles. Such region is marked as ‘C’.

In yet another type of questions on Venn-diagram a complex geometrical figure is provided and you are required to count the number of triangles, rectangles and squares respectively. Consider the example given below:

**Ex.** How many triangles are there in the following figures ABCD?

**Answer:** First of all label the diagram completely and then starts counting the number of triangles:

The triangles are: AFB, DFC, BFC, AFD, AEF, EFD, DFG, CFG, ADC, ABC, BDC, ABD

Thus, there are 12 triangles.

**Ex**- Which diagram represents the relationship among female, mothers and doctors?

**Solution:-** (3) Some females may be mothers.

Some females may be doctors.

All mothers are females.

Some doctors may be mothers.

**Ex**- Which number is common in the square, ellipse and triangle?

**Solution**:- (4) The number ‘7’ is common to the square, ellipse and triangle.

**Ex**- How many triangles are there in the given figure?

**Solution:**- The triangles are:

DEAB; DFBC; DGCD; DHAD; DADC; DBCD; DABC; DABD; DMAB; DMBC; DMCD; DMAD; DEAI; DEBI; DBFJ; DFCJ; DGCK; DGDK; DHDL; DHAL; DAHM; DDHM; DBFM; DCFM; DALM; DMLD; DBMJ; DMCJ

So, there are 28 triangles.