Set Theory | Logical Reasoning (LR) and Data Interpretation (DI) - CAT PDF Download

Logical diagrams based situations have their own importance in the context of preparing for any aptitude examination. There are three major types of questions based on diagrams —
(i) Numerical questions on set theory based on venn diagrams
(ii) Logical questions based on set theory
(iii) Questions based on network diagrams.
Let us first take a look at some standard theoretical inputs related to set theory.

Look at the following diagrams:

Figure 1: Refers to the situation where there are two attributes A and B. (Let’s say A refers to people who passed in Physics and B refers to people who passed in Chemistry.) Then the shaded area shows the people who passed both Physics and Chemistry.
Set Theory | Logical Reasoning (LR) and Data Interpretation (DI) - CAT

In mathematical terms, the situation is represented as:
Total number of people who passed at least 1 subject = A + B – A ∩ B
Figure 2: Refers to the situation where there are three attributes being measured. In the figure below, we are talking about people who passed Physics, Chemistry and/or Mathematics.
Set Theory | Logical Reasoning (LR) and Data Interpretation (DI) - CAT

In the above figure, the following explain the respective areas:
Area 1: People who passed in Physics only
Area 2: People who passed in Physics and Chemistry only (in other words— people who passed Physics and Chemistry but not Mathematics)
Area 3: People who passed Chemistry only
Area 4: People who passed Chemistry and Mathematics only (also, can be described as people who passed Chemistry and Mathematics but not Physics)
Area 5: People who passed Physics and Mathematics only (also, can be described as people who passed Physics and Mathematics but not Chemistry)
Area 6: People who passed Physics, Chemistry and Mathematics
Area 7: People who passed Mathematics only
Area 8: People who passed in no subjects
Also take note of the following language which there is normally confusion about:
People passing Physics and Chemistry—Represented by the sum of areas 2 and 6
People passing Physics and Maths—Represented by the sum of areas 5 and 6
People passing Chemistry and Maths—Represented by the sum of areas 4 and 6
People passing Physics—Represented by the sum of the areas 1, 2, 5 and 6
In mathematical terms, this means:
Total number of people who passed at least 1 subject =
P + C + M – P ∩ C – P ∩ M – C ∩ M + P ∩ C ∩ M

Let us consider the following question and see how these figures work in terms of real time problem solving:
Q.1. 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?
(a) 35 
(b) 75 
(c) 55 
(d) 25

Set Theory | Logical Reasoning (LR) and Data Interpretation (DI) - CAT
From the figure, it is clear that the number of people at the party were 30 + 10 +15 = 55.
We can of course solve this mathematically as below:
Let n(A) = No. of persons who kissed Sherry = 40
n(B) = No. of persons who shake hands with Sherry = 25
and n(A ∩ B) = No. of persons who shook hands with Sherry and kissed him both = 10
Then using the formula, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
n(A ∪ B) = 40 + 25 – 10 = 55


Q.2. In the Mindworkzz club all the members participate either in the Tambola or the Fete. 320 participate in the Fete, 350 participate in the Tambola and 220 participate in both. How many members does the club have?
(a) 410 
(b) 550
(c) 440 
(d) None of these

Set Theory | Logical Reasoning (LR) and Data Interpretation (DI) - CAT
The total number of people = 100 + 220 + 130 = 450
Option (d) is correct.

The document Set Theory | Logical Reasoning (LR) and Data Interpretation (DI) - CAT is a part of the CAT Course Logical Reasoning (LR) and Data Interpretation (DI).
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FAQs on Set Theory - Logical Reasoning (LR) and Data Interpretation (DI) - CAT

1. What is set theory?
Ans. Set theory is a branch of mathematical logic that deals with the study of sets, which are collections of objects or elements. It provides a foundation for mathematical analysis and helps in understanding various mathematical concepts and structures.
2. How are sets defined in set theory?
Ans. In set theory, sets are defined as a well-defined collection of distinct objects, called elements, which can be anything from numbers to colors or even other sets. Sets are usually denoted by listing their elements within curly braces, separated by commas.
3. What are the basic operations in set theory?
Ans. Set theory includes several basic operations that can be performed on sets. These operations include union, intersection, complement, and difference. The union of two sets is the combination of all the elements from both sets, the intersection is the common elements between two sets, the complement is the set of elements not belonging to a particular set, and the difference is the elements only in one set but not the other.
4. How does set theory relate to other branches of mathematics?
Ans. Set theory serves as a foundation for various branches of mathematics, including algebra, calculus, and logic. It provides a framework to define and study mathematical objects and structures. Many mathematical concepts, such as functions, relations, and numbers, can be defined and analyzed using set theory.
5. What are some applications of set theory?
Ans. Set theory has numerous applications in various fields. It is used in computer science for database management, artificial intelligence, and programming languages. Set theory is also applied in statistics, probability theory, linguistics, and formal logic. It provides a powerful toolset for analyzing and modeling relationships between different elements or entities.
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