Solved Examples on Roster Form
Problem 1: Find the correct roster form of the set of first three prime numbers from the following:
A = {1, 2, 3}
A = {2, 3, 5}
A = {2, 3, 4}
Solution:
First three prime numbers are 2, 3 and 5.
In roster form, A= {2,3,5}
Problem 2: Write the following sets in roster form.
a. Days in a week
b. First 5 natural numbers
Solution:
Days in a week => A = {Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}
First 5 natural numbers => B = {1,2,3,4,5}
Problem 3: Express the set A = {x | x = 2n2 – 2, where n ∈ N and n < 5} in roster form.
Solution:
The elements of set A are:
For n = 1, 2n2 − 2 = 2 × 12 −2 = 0
For n = 2, 2n2 − 2 = 2 × 22 − 2 = 6
For n = 3, 2n2 − 2 = 2 × 32 − 2 = 16
For n = 4, 2n2 − 2 = 2 × 42 − 2 = 30
For n = 5, 2n2 − 2 = 2 × 52 − 2 = 48
A = {0, 6, 16, 30, 48}
Problem 4: Convert the following set from set builder notation into roster notation: P = {x | x is a prime number less than 15}.
Solution:
We know that the prime numbers less than 15 are 2, 3, 5, 7, 11 and 13.
Therefore, the given set in roster form is {2, 3, 5, 7, 11, 13}.
Roster Form
Roster Form is one of the two representations that any set can have, with the other representation being Set-Builder Form. In Roster form, all the elements of the set are listed in a row inside curly brackets. If the set comprises more than one element, a comma is used in roster notation to indicate the separation of every two elements. Since each element is counted separately, the roster form is also known as Enumeration Notation.
This article explores the concept of Roster form and helps you learn about this method of representing sets in Set Theory. In addition to details about Roster Form, we will also cover notation, provide examples, and discuss various applications of Roster Form.
Table of Content
- What is Roster Form in Sets?
- Roster Notation
- Limitations of Roster Notation
- Roster and Set Builder Form
- Examples on Roster Form
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