Question

Explain with examples how to convert roaster form to set and builder and set builder to roaster? ​

Answer 1

Answer:

Roster Form :

Listing the elements of a set inside a pair of braces { } is called the roster form.

(i) Let A be the set of even natural numbers less than 11.

In roster form we write A = {2, 4, 6, 8, 10}

(ii) A = {x : x is an integer and- 1≤ x < 5}

In roster form we write A = {-1, 0,1, 2, 3, 4}

Let us look into some examples in roster form.

Set Builder Form :

Set-builder notation is a notation for describing a set by indicating the properties that its members must satisfy.

Reading Notation :

‘|’or ‘:’ such that

A = { x : x is a letter in the word dictionary }

We read it as

“A is the set of all x such that x is a letter in the word dictionary”

For example,

(i) N = "x : x is a natural number,

(ii) P = "x : x is a prime number less than 100,

(iii) A = "x : x is a letter in the English alphabet,

Here we are going to see examples on roster form and set builder form.

Roster Form Examples

Example 1 :

List the elements of the following set in Roster form:

The set of all positive integers which are multiples of 7

Solution :

The set of all positive integers which are multiples of 7 in roster form is

{7, 14, 21, 28,...........}

Example 2 :

List the elements of the following set in Roster form:

The set of all prime numbers less than 20.

Solution :

The set of all prime numbers less than 20 in roster form is

{2, 3, 5, 7, 11, 13, 17, 19}

Example 3 :

Write the set A = { x : x is a natural number ≤ 8} in roster form.

Solution :

A = { x : x is a natural number ≤ 8}.

So, the set contains the elements 1, 2, 3, 4, 5, 6, 7, 8.

Hence in roster form A = {1, 2, 3, 4, 5, 6, 7, 8}

Example 4 :

Write the following set in roster form

A = {x : x ∈ N, 2 < x ≤ 10}

Solution :

A = {x : x ∈ N, 2 < x ≤ 10}

Set A will contain elements greater than 2 and less than or equal to 10.

A = { 3, 4, 5, 6, 7, 8, 9, 10}

Example 5 :

Write the following set in roster form

X = {x : x = 2n, n ∈ N and n ≤ 5}

Solution :

X = {x : x = 2n, n ∈ N and n ≤ 5}

Answer 2

Answer:

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