Select problems from exercise 2.2

solutions to a few problems from NCERT exercise.

In this article we will look at solutions of a few selected problems from exercise 2.2 of NCERT.

Problem 1:

Let

R

be the relation on

Z

defined by

R = {(a, b) : a, b \in Z, a - b

is an integer

}

. Find the domain and range of

R

Note: $Z$ ‍ is the set of integers.

Solution:

Recall that domain is the set of all first elements and range is the set of all second elements of ordered pairs in the relation.

First we need to think of what all ordered pairs the relation

R

will have.

Let's pick

a = 1

. Now

1 - 0

1 - 3

1 - (- 5)

and

1 - 6

are all integers. In fact

1 -

(any integer) is an integer. Thus

1

pairs with all integers.

Now choose any other integer value for

a

. See that this

a

will also pair with all integers.

Thus the final relation

R

will look something like:

\begin{aligned} R = {\dots \dots \dots \dots \dots, \\ \dots (- 1, - 1), (- 1, 0), (- 1, 1), (- 1, 2) \dots, \\ \dots (0, - 1), (0, 0), (0, 1), (0, 2) \dots, \\ \dots (1, - 1), (1, 0), (1, 1), (1, 2) \dots, \\ \dots \dots \dots \dots \dots} \end{aligned}

All integers will appear in the first elements' place, and that too multiple times. Similarly all integers will appear in the second elements' place, and that too multiple times.

Thus for the given relation, domain is

Z

, and range is

Z

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