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Explain Remarks

**Remarks ** (i) A relation may be represented algebraically either by the Roster method or by the Set-builder method.

(i) An arrow diagram is a visual representation of a relation.

Hi,

Point number 2 of the remark:

Here author is saying that if once we have established the relation R that from your question is

Now visually we can represent it via diagram as shown below

POINT No. 1 :

Algebraic means that is represented in some variables so Roster or set builder method are the methods by which statements can be represented in different form than question asked.

In

**set builder form**, the set is described by a characterizing property of its elements. In order to describe a set, a variable, say*x*is written inside the braces and then after putting a colon the common property*P*(*x*) possessed by each element of the set is written within the braces.**Example:**

The set

*P*= {1, 2, 3, 4, 5, 6, 7, 8} can be written in set builder form as*P*= {*x*:*x*ε N,*x*≤ 8}The set

*Q*= {1, 4, 9, 16... 100} can be written in set builder form as*Q*= {*x*^{2}:*x*ε N, 1 ≤*x*≤ 10}In

**roster form**, the set is described by listing elements, separated by commas, within the braces { }.**Example:**

Let A = {

*x*:*x*is a set of even natural numbers between 15 and 45} .Write this set in roster forms.A = {

*x*:*x*is a set of even natural numbers between 15 and 45}.The roster form of this set can be written as:

A = {16, 18 20 22, 24 26, 28, 30, 32, 34, 36, 38, 40, 42, 44

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