OBSERVATIONAL SKILLS

Introduction:

This section consists of questions that require keen observation skills and analysis of the given data.

The questions can be simplified with the help of venn diagrams or some charts or anything that simplifies the data for analysis.

This chapter can be divided broadly into below 3 topics:

1. Venn Diagram

SET : Collection of well defined objects are called SET.

Example :

(i) Set of numbers 1 , 3 , 5 , 7 , 9 , 11

(ii) Set of vowels in the alphabets of English

(iii) Set of rivers in India

(iv) Set of Life Science books in IFAS Library

(v) Set of multiples of 4 (i.e. 4 , 8 , 12 , 16 , ....)

UNIVERSAL SET : If all the given sets are subsets of a set U, then the set U is called Universal Set.

Example 1: Draw a Venn diagram to represent the following sets:

U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 5, 6}, B = {3, 9}

Step 1 : Draw a rectangle and label it U to represent the universal set.

Step 2 : Draw circles within the rectangle to represent the other sets. Label the circles and write the relevant elements in each circle.

Step 3 : Write the remaining elements outside the circles but within the rectangle.

Operations on Sets

(1) Union of Sets (A U B):

Let A and B be two given Sets. Then the union of A and B is the set of all those elements which belongs to either A or B or both.

n(A U B) = n(A) + n(B) - n(A ∩ B)

(2) Intersection of Sets (A ∩ B):

Let A and B be two given Sets. Then the intersection of A and B is the set of elements which belong to both A and B.

(3) Differences of Sets (A - B):

Let A and B be two given Sets.The difference of Set A and B is the Set of elements which are in A but not in B.

Example 2: At the birthday party of Sherry, a baby boy, 40 persons chose to kiss him and 25 chose to shake hands with him. 10 persons chose to both kiss him and shake hands with him. How many persons turned out at the party?

Represent the data in the form of venn diagram as below:

It is clear that the number of people at the party were 30 + 10 + 15 = 55.

Example 3: There are 20000 people living in Palam Vihar , Gurgaon. Out of them 9000 subscribe to Star TV Network and 12000 to Zee TV Network. If 4000 subscribe to both, how many do not subscribe to any of the two?

Given:

Total people living in Palam Vihar = 20,000

People subscribe to Star TV Network = 9000

People subscribe to Zee TV Network = 12000

People subscribe both Star TV and Zee TV Network = 4000

Represent the data in the form of venn diagram as below:

From diagram . its clear that 5000 people subscribe Star TV , 8000 people subscribe Zee TV and 4000 people subscribe both Zee and Star TV.

So total people subscibe atleast 1 = 5000 + 8000 + 4000 = 17000

So total people which do not subscribe any of the two network = 20,000 - 17,000 = 3000

Few Possible Cases of Venn Diagram :

1) There will be a series of sub cases one under another.

We know that day is a part of the week and week is the part of the month.

2) One main category, under it two sub categories and both bear no similarities among them.

Here, in animals we have many species of which cat and dog are two different kind of species, having nothing in common.

3) One main category, under it two sub categories and both bear some similarities among them.

Liquids > Petrol, diesel. Here both are flammables in nature, thus bear similarity.

4) Three sections having no common feature.

We know that Mars, Earth and Jupiter are three independent entities having nothing in common.

5) There is a chance of finding a common place that satisfies all the properties of three individual sections.

A women can be Mother (A) , Step-Mother (B) and Sister-in-law (C)

A women at the same time can be Mother and Step-Mother (D)

A women at the same time can be Mother and Sister-in-law (E)

A women at the same time can be Step-Mother and Sister-in-law (F)

A women at the same time can be Mother , Step-Mother and Sister-in-law (G)

6) Among three different sections, two may have some common properties those do not match with third one.

From the above, actor and headmaster are showing masculinity, thus bearing some common properties which is just opposite to Queen.

7) Cases in which out of three sections, two are inter related as parent child relationship, whereas third one has no relation with them.

Tree > Mango Tree > Dog. We all know Mango tree is coming under tree category but animal Dog has nothing to do with these 2 words.

8) One category may have one sub category. They both partially satisfy some conditions (not always).

Vegetable>Capsicum>Red. Some capsicums are red and so as some other vegetables.

Example 4: Which of the following diagrams correctly represents the relationship among tennis fans, cricket players and Students?

From the relationship given in the question, we observe that each of the objects carries something in common to one another. A Tennis fan can be a cricket player as well as student. Hence Diagram (1) represents this relationship.