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