How to do Sets in Math

Introduction to do sets in math:

A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics. Set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. Let us see about the concept of how to do sets in math. (Source: Wikipedia)

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Sets in math:


By using two methods we can do the sets in math. They are,

Roster or tabular form
Set-builder form
How to do sets in math by using Roster form:

The elements are separated by using the commas, and the elements are placed inside of braces { }. For example, the set of all odd positive integers less than 8 is expressed in roster form as {1, 3, 5, 7}.

How to do sets in math by using Set-builder form:

For example, in the set {1, 3, 5, 7, 11}, all the elements possess a common property, namely, all are prime number, which are not possessed in any other set. Representing this set by P, we write P = {x: x is a prime numbers in real numbers}


Example problem in set:


Problem1: Find the solution set of the following equation by using roster form x 2 + x – 2 = 0.

Solution:

x 2 + x – 2 = 0 can be expressed as (x – 1) (x + 2) = 0, that is x = 1, – 2.

Therefore, the solution is {1, – 2}.

Problem 2: Find the set {x: x is a positive integer and x2 < 30} in the roster form.

Solution:

By the given we need the following numbers to represent the set -1, 2, 3, 4, 5.

So, the given set in the roster form is {1, 2, 3, 4, 5}.

Problem 3: Find the set A = {1, 4, 9, 16, 25 . . .} by using set-builder form.

Solution:

We may write the set A as A = {x: x is the square of a natural number}

Alternatively, we can write A = {x: x = n2, where n ∈ N}

In this section we have seen about the concept of how to do sets in math.