Set Operation is one of the important topics covered in GMAT exam. Before we go into operations on set elements, let us look at some basic representations.
Set is represented by Capital Letters and small letters denote the members. There are two methods of representing a set – Rooster and Builder Method.
Rooster Method
In rooster method, we represent the set starting with the Set Name in Capital letter followed by an equal sign, a curly opening brace, members of the set and finally closing the set members with curly closing braces. For a Set representation of first five alphabets in English, the rooster representation will be:
A = {a, b, c, d, e}
Set Builder Method
Instead of listing the set members, the set builder method defines the properties of the members. This method is also called the Property method.
For Example, if we want to represent the set of all odd integers, we represent the set starting with the Set Name in capital letter followed by an equal sign, curly opening braces, property of the set and finally closing the set representation with curly closing braces. The Set Builder Method of representing a set of odd integers would be:
A = {2i+1: i is an integer}
As you can see above, the property of the Set follows the format
Representation of Set Members in a Formula: property of variable(s) in the Formula
"|" can be used instead of ":" for Set Builder Method.
Let us look at another Set Builder Method Representation, where we start with the Set Name, followed by opening braces, variable name, the member representation (Integer or Real Number or Alphabet) followed by the formula.
Z is the representation of Integers and R is the representation of Real numbers.
A = {i Z: 2i + 1} where Z represents integers.
Let us look at another representation of real numbers less than 9 and greater than 5.
A = {x R: x >5 and x < 9} is a set of real numbers greater than 5 but less than 9 and R represents real numbers.
Summary of Number Types in Set Builder Method
- Integers - Z
- Natural Numbers - N
- Rational Numbers - Q
- Real Numbers - R
- Imaginary Numbers - I
- Complex Numbers - C
