#### Set Theory

Importance of that topic in various exams

Set theory and Venn Diagrams are one of the most commonly tested topics in MBA exams. Questions from the Set theory have appeared consistently in the CAT, XAT, GMAT exam for the last several years. Set theory and Venn diagram is a very interesting topic, as it is also useful in Data Interpretation and Logical Reasoning

#### CAT :

 Set Theory Year Slot No of Questions Good attempt Difficulty 2019 Slot 1 4 2 Moderate Slot 2 3 2 Difficult 2018 Slot 1 4 4 Easy Slot 2 4 3 Moderate 2017 Slot 1 4 3 Easy Slot 2 4 3 Easy

#### XAT :

 Year No of Questions Good attempt Difficulty 2019 2 2 Moderate 2018 1 1 Easy 2017 3 2 Moderate-Difficult

IIFT

 Year No of Questions Good attempt Difficulty 2019 3 2 Moderate 2018 1 1 Moderate 2017 2 1 Difficult

SNAP

 Year No of Questions Good attempt Difficulty 2019 6 4 Moderate 2018 4 1 Moderate 2017 4 2 Difficult

### Some Questions from Previous Papers

1. There are 30 students in a class. Among them, 8 students are learning both English and French. A total of 18 students are learning English. If every student is learning at least one language, how many students are learning French in total? (XAT 2018)

The Venn diagram for this problem looks like this.

Every student is learning at least one language. Hence there is no one who fall in the category‘neither’.

So in this case, n(EᴜF) = n(µ).

It is mentioned in the problem that a total of 18 are learning English. This DOES NOT mean that 18 are learning ONLY English. Only when the word ‘only’ is mentioned in the problem should we consider it so.

Now, 18 are learning English and 8 are learning both. This means that 18 – 8 = 10 are learning ONLY English.

n(µ) = 30, n(E) = 10

n(EᴜF) = n(E) + n(F) – n(E∩F)

30 = 18+ n(F) – 8

n(F) = 20

Therefore, total number of students learning French = 20.

2. Set Fn gives all factors of n. Set Mn gives all multiples of n less than 1000. Which of the following statements is/are true? (CAT 2019, Slot 1)

a. F108 ∩ F84 = F12

b. M12 ∪ M18 = M36

c. M12 ∩ M18 = M36

d. M12 ⊂ (M6 ∩ M4)

• a, b, and c only

• a, c and d only

• a and c only

• All statements are true

F108 ∩ F84

This is the set of all numbers that are factors of both 108 and 84

=> this is set of all common factors of 84 and 108

=> this is set of numbers that are factors of the Highest Common Factor of 84 and 108.

HCF (84, 108) = 12

F108 ∩ F84 = F12 – this is true

M12 will have numbers {12, 24, 36, 48, ….} Numbers like 12, 24, … will not feature in M36. So, Statement B cannot be true.

M12 ∩ M18 – this is the set of all common multiples of 12 and 18.

This is the set of numbers that are multiples of the Least Common Multiple of 12 and 18. (which is 36).This statement is also true. iv. Using the same logic as that used in statement iii, we can determine that statement iv is also true. Remember that every set is a subset of itself.

3. In a class 40% of the students enrolled for Math and 70% enrolled in Economics. If 15% of the students enrolled for both Math and Economics, what % of the students of the class did not enroll for either of the two subjects? (SNAP 2019)

a) 5%

b) 15%

c) 0%

d) 25%

We know that (A U B) = A + B – (A n B), where (A U B) represents the set of people who have enrolled for at least one of the two subjects Math or Economics and (A n B) represents the set of people who have enrolled for both the subjects Math and Economics.

(A U B) = A + B – (A n B) => (A U B) = 40 + 70 – 15 = 95%

That is 95% of the students have enrolled for at least one of the two subjects Math or Economics.

Therefore, the balance (100 – 95)% = 5% of the students have not enrolled for either of the two subjects.

4. In a survey it was found that 10% people don’t use Facebook, Twitter or Whatsapp.8% uses all the three. There are 15% who uses Facebook and Twitter, 20% who use Twitter and Whatsapp and 20% who useFacebook and Whatsapp. The number of people that use only Facebook, only Twitter and only Whatsapp is equal. If the survey was conducted on 1000 people, answer the following :

What is the ratio of a number of people that uses Whatsapp only to the people using either Whats app or Facebook or both? (CAT 2019, Slot 2)

a) 1/6

b) 25/75

c) 1/9

d) 1/3

Let the no. of people that use only Facebook = only Twitter = only Whatsapp = x

Let’s construct of Venn diagram:

From the figure we can see that x + x + x + 8 + 20 + 20 + 15 + 10 = 100

=) 3x = 100 – 73

=) x = 27/3 = 9

Thus the of no people who use Whatsapp only = 9% or 9 x 1000/100 = 90

% of people that use Whatsapp only = 9

% of people that use either Whatsapp or Facebook or both = 20 + 20 + 8 + 9 + 9 +15 = 81 Thus the ratio = 9/81=1/9

### How to deal with that topic preparation

Level 1

• List out the formula related to the topic and focus on understanding the fundamentals and application
• Break down the steps and simplify the process to understand a question. Practice almost 50-60 questions each for a particular concept
• Always look for a definite answer

Level 2

• Watch tutorials for a better understanding
• Practising is the only way to master the Set Theory topic
• Understand the concepts and learn how to apply them in different applications

Level 3

Students need to look into problems that use multiple concepts to find a solution. Try to answer questions from the advanced level of previous CAT papers, mock tests, and materials. And, try to attempt these questions in a time-based manner. Taking too much time for advanced questions will not be considered good to crack the exam. Finally, Practice is the only key to success.