Problem 97 - Introductory and Intermediate Algebra for College Students 4th

Question

What is a set?

Step-by-Step Solution

Answer

A set is a collection of distinct objects, considered as an object in its own right. Sets are symbolized by upper-case letters, and its elements are represented in lowercase. They can be expressed in two ways: Roster (Listing) method, where all elements of the set are listed inside braces, and Set builder method, where a rule that describes the elements is stated.

Step 1: Understanding a Set

In mathematics, a set is a collection of distinct objects. These objects are referred to as elements or members of the set. A set can be symbolized by an uppercase letter and its elements represented in lowercase. It can be expressed in two ways: Roster (Listing) method, where all members are listed inside braces, and Set-builder method, where a rule that describes what is included in the set is stated.

Step 2: Examples of a Set

An example of a set using the Roster method could be: A = {1, 2, 3, 4}. 'A' is the set that contains four elements, namely numbers 1,2,3,4. An example of a set using the Set-builder method could be: B = {x : x is a natural number less than 5}. 'B' is the set that contains natural numbers that are less than 5, therefore, the members of 'B' set are: 1, 2, 3, 4.