A relation R is defined on the set Z of integers as follows- x- y - R- x2-y2- 25 Express R and R-1 as the sets of ordered pairs and hence find their respective domains-

y= ±√(25 x^2) where both x and y are integers.Cleraly for x= 0,± 3, ± 4, ± 5 , y will be integers as y = ± 5, ± 4, ± 3, 0 ∴ R = (0, ± 5), (± ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Domain

A relation R ...

Question

A relation R is defined on the set Z of integers as follows: (x, y) $\in R^{'} x^{2} + y^{2} = 25$
Express R and $R^{- 1}$ as the sets of ordered pairs and hence find their respective domains.

Open in App

Solution

$y = \pm \sqrt{25 - x^{2}}$
where both x and y are integers.
Cleraly for $x = 0, \pm 3, \pm 4, \pm 5$ , y will be integers as
$y = \pm 5, \pm 4, \pm 3, 0$
$∴ R = (0, \pm 5), (\pm 3, \pm 4), (\pm 4, \pm 3), (\pm 5, 0)$
$R^{- 1} = (\pm 5, 0), (\pm 4, \pm 3), (\pm 3, \pm 4), (0, \pm 5)$
Each R and $R^{- 1}$ consists of 2+ 4 + 4 +2 = 12 ordered pairs.
Domain of R ={ $0, \pm 3, \pm 4, \pm 5$ } = domain of $R^{- 1}$ .

Suggest Corrections

Similar questions

Q. A relation

R

is defined on the set

Z

of integers as follows: R=

(x, y)

\in R : x^{2} + y^{2} = 25

. Express

R

and

R^{- 1}

as the sets of ordered pairs and hence find their respective domains.

Q. A relation R is defined on the set

z

of integers as follows.

(x, y) \in R \Leftrightarrow x^{2} + y^{2} = 25

. Express

R

and

R^{- 1}

as the set of ordered pairs and hence find their respective domains.

Let A be the set of first natural numbers and let R be a relation on A defined as follows :

$(x, y) ϵ R \Leftrightarrow x \leq y$

Express R and $R^{- 1}$ as sets of ordered pairs. Determine also

(i) The domain of $R^{- 1}$

(ii) The range of R.

Q. A relation

R

is defined from a set

A = [2, 3, 4, 5]

to a set

B = [3, 6, 7, 10]

as follows:

(x, y) \in R \Leftrightarrow x

is relatively prime to

y

.Express R as a set of ordered pairs and determine its domain and range.

A relation R is defined from a set A = {2, 3, 4, 5} to a set B = {3, 6, 7, 10} as follows : ${x, y} ϵ R \Leftrightarrow x$ is relatively prime to y. Express R as a set of ordered pairs and determine its domain and range.

Join BYJU'S Learning Program

A relation R is defined on the set Z of integers as follows: (x, y)∈R′x2+y2=25 Express R and R−1 as the sets of ordered pairs and hence find their respective domains.

y=±√25−x2where both x and y are integers.Cleraly for x=0,±3,±4,±5, y will be integers asy=±5,±4,±3,0∴R=(0,±5),(±3,±4),(±4,±3),(±5,0)R−1=(±5,0),(±4,±3),(±3,±4),(0,±5)Each R and R−1 consists of 2+ 4 + 4 +2 = 12 ordered pairs.Domain of R ={0,±3,±4,±5} = domain of R−1.

A relation R is defined on the set Z of integers as follows: (x, y) $\in R^{'} x^{2} + y^{2} = 25$
Express R and $R^{- 1}$ as the sets of ordered pairs and hence find their respective domains.