Representation of a Function in Roster form

Sets are known as groups of well-defined information. In mathematics, a set is a tool that helps classify and collect data that belongs to the same category, even if the elements used in sets are all different. Still, they are all similar because they belong to the same group. Sets can be depicted in two ways – roster form and set-builder form. This article will discuss the representation of a function in roster form and good roster form.  

What is a roster set?

The elements in roster form are enclosed by curly brackets {}. The brackets contain all of the elements that are mentioned and separated by commas. The roster form is the simplest way to represent data in groups.

An example for a set of tables for 5 is 

A = {5, 10, 15, 20, 25, 30, 35…..}.

A few properties of good roster form is mentioned below:

• The roster form’s arrangement does not have to be in the same order. An example can be A= {a, b, c, d, e} is equal to A= {e, d, a, c, b}.

• There is no repetition in roster form – the components are not repeated; for example, the word “apple” will be written as A= {a, p, l, e}. 

• Finite sets are depicted either with all of the elements or, if the elements are too numerous, like dots in the middle. The infinite sets are usually illustrated by dots at the end. 

Solved Example Of Roster Set

Question 1

The figure given below gives a relationship between the two P and Q. State the relation between:

1. set-builder form

2. Roster form

Write what domain and range are.

Solution

The distinction between x and y,  which is 2, defines the relationship between P and Q.

R={(x,y):x-y=2,x∈P, y∈Q} in set builder form

R = {(5, 3), (6, 4), (7, 5)} in roster form

This relation’s domain is {5, 6, 7.}

This relationship has a range of {3, 4, 5}

Question 2

Convert the given relation into roster form. 

R = (x, x3): (x is a prime number less than 10.)

Solution

Given, R = (x, x3): x is a prime number less than ten.

Therefore,

R = {(2, 8), (3, 27), (5, 125), and (7, 343)}

Question 3

Write the following data into the roster form.

1. Natural numbers

2. Numbers that are greater than 6 but less than 3.

3. All even numbers between 10 and 25.

Solution

The roster form contains the information mentioned above.

Set A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11……}

Set B= {}  Null Set, Because there are no numbers greater than 6 and less than 3

Set C= {10, 12, 14, 16, 18, 20, 22, 24.}

Question 4

The following sets are in roster form; convert them into set-builder form.

A= {b, c, d, f, g, h, j, k, l, m, n, p, q, r, s, t, v, w, x, y, z}

B= {2, 4, 6, 8, 10}

C= {5, 7, 9, 11,13, 15, 17, 19}

Solution

The answer to the above sets into the set builder form is given below.

A= {a: a is a consonant of the English Alphabet}

B= {b: b is an even number and 2≤ b ≤10}

C= {c: c is an odd number and 5≤ c ≤ 19}

Question 5

Give examples for the mentioned sets in both roster and set-builder form.

1. Singular Set.

2. Finite Set.

3. Infinite Set.

Solution

You can choose any example for the sets mentioned above as there are many of them. 

1. Singular Set

Roster Form: A= {2}

Set-builder form: A= {a: a∈N and 1<a<3}

2. Finite Set

Roster Form: B= {0,1, 2, 3, 4, 5}

Set-builder form: B= {b: b is a whole number and b<6}

3. Infinite Set

Roster Form: C= {2, 4, 6, 8, 10, 12, 14, 16…..}

Set- builder form: C= {c: c is a natural and even number}

Question 6

State the order of the given sets

A= {7, 14, 21, 28, 35}

B= {a, b, c, d, e, f, e….x, y, z}

C= {2, 4, 6, 8, 10, 12, 14……}

Solution

The order of the set indicates the number of elements in the set.

Set A has five elements, so its order is five.

Set B’s order is 26 because the English alphabet has 26 letters.

Set C has an infinite number of elements, so its order is infinite.

Question 7

Write the given sets in roster form.

A = {a: a = n/2, n ∈ N, n < 10}

B = {b: b = n2, n ∈ N, n ≤ 5}

Solution

The above sets can be written in roster form as follows.

A= {1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, 9/2}

B= {1, 4, 9, 16, 25}

Conclusion

Roster form is the best way to represent finite sets. Sets are known as groups of well-defined information. In mathematics, a set is a tool that helps classify and collect data that belongs to the same category, even if the elements used in sets are all different. Still, they are all similar because they belong to the same group. The details of a set are represented in a row surrounded by curly brackets in roster notation. If the set contains more than one element, commas separate every two elements. Suppose A is a set of natural numbers then A can be represented by A= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. In this article, we have discussed the representation of a function in roster form.