# Worked Examples

Example-1

Items contained in one another.

Solution

Squares are represented by circle X. Rectangles are represented by circle Y and quadrilaterals are represented by circle Z.

We know that all squares are rectangles and all rectangles are quadrilaterals. Accordingly, circle X is inside circle Y and circle Y is inside circle Z.

Example-2

One item contains the other two items, which are different from each other.

For example, Parrot, Dove, Birds

Solution

It is clear that parrot (X) and dove (Y) are separate items and both are birds (Z).

Example-3

One item contains the other item and the third item shares some common features with the other two items.

For example, Cow, Animal, White

Solution

Clearly, all cows (X) are animals (Y).
This is represented by two concentric circles.
However, some cows and some animals can be white in colour (Z).

So, circle Z which represents white intersects the other two concentric circles.

Example-4

All the three items have some common features.

For example, Women, Politician, Smart

Solution

Clearly, all the three are inter-related.
Some women (X) may be politicians (Y) and some may be smart (Z).
Similarly, some politicians may be smart and may be women.
So, all the three circles intersect with each other.

Example-5

Independent items.

For example, Fruits, Vehicles, Animals

Solution

These three items bear no relationship to each other.
So they are represented by three disjoint circles.

Example-6

One item is contained in the other, while the third item is entirely different from the two.

Solution

Clearly, all plums (X) are fruits (Y) and bread (Z) is entirely different.

Example-7

Two independent items sharing some common feature with the third item.

For example, Boys, Girls, Educated

Solution

It is obvious that only some boys are educated and some girls are educated, and no boy is a girl and vice-versa.
X represents boys, Y represents educated and Z represents girls.

Example-8

One item is contained in another item and the third item shares some of the features only with second item.

For example, Water, Liquids, Elements

Solution

Liquids, water and elements are represented by circles X, Y and Z, respectively.
Since water is a liquid, circle Y lies inside circle X.
Some of the elements (but not all the elements) are liquids.
So, circles X and Y intersect. Water is not an element.
So, circles Y and Z do not intersect with each other.

Example-9

One item is partially contained in the other and the third item is fully contained in both.

For example, Furniture, Wooden materials, Wooden chair

Solution

Furniture, wooden materials and wooden chair are represented by circles X, Y and Z, respectively.
Some of the furniture is made up of wood.
So, circles X and Y intersect with each other.
Wooden chair is furniture as well as a wooden material.
So, circle Z lie inside both the circles X and Y.

Example-10

One item is partially contained in the other item and the third item is independent.

Solution

Clearly, some teachers (X) are graduates (Y), but vehicles (Z) are neither teachers nor graduates.

Example-11

One item is partially contained in the other item and both these items are contained in the third item.

For example, Politicians, Agriculturists, Human beings

Solution

Politicians (X) and agriculturists (Y) are part of human beings (Z).
But some politicians are agriculturists and some agriculturists are politicians.