Set Theory

Basics of set language theory such as union of sets, intersection of sets get tested in the GMAT problem solving and data sufficiency sections. With a good grasp of the basic formulae governing set language, one should be able to attempt these questions with ease. 4GMAT's GMAT Math Lesson Book in this chapter covers the following concepts

1. Introduction of the concept of sets and methods to represent sets.
2. Different types of sets explained with illustrative examples.
3. Cardinal number of sets, power sets, number of subsets for a set.
4. The De-Morgan's Law.
5. Using Venn Diagrams to solve set language questions explained with illustrative examples.
6. 7 solved examples, including Venn Diagram representation.
7. 5 Comprehensive exercise problems with answer key and explanatory answers.
8. An objective type speed test with around 35 questions along with explanatory answers and answer key are provided for the speed test.

Here is an example of a typical solved example in this chapter.
Sample Question
Question
In a room of 50 people whose dresses have either red or white color, 30 are wearing red dress, 16 are wearing a combination of red and white. How many are wearing dresses that have only white color?

Explanatory Answer
Venn Diagram Number of people wearing a red dress = 30
i.e., n(R) = 30

Number of people wearing a combination of red and white = 16
i.e., n (R Intersection W) = 16

The total number of people in the room = number of people who are wearing dresses that have either red or white color = n (R Union W) = 50.

We know,
n (R Union W) = n(R) + n(W) - n(R Intersection W)
50 = 30 + n(W) - 16
50 - 14 = n(W) - 16
n(W) = 36
i.e., the number of people who are wearing a white dress = 36.

Therefore, number of people who are wearing white dress only = n(W) - n(R Intersection W) = 36 - 16 = 20
Additional Practice Questions in Set Language
Looking for additional practice questions in Set Theory? A collection of some questions available at