A Relation R is defined in the set of integers I as follows -x-y- - R if x-2 - y-2 - 9 which of the following is false-

Explanation for the correct option:Given, x^2 + y^2 = 9, (x,y) ∈ R⇒ x = √(9 – y^2)Therefore, set of R={(0,3),(0, 3),(3,0),( 3,0)}⇒Domain of R={ 3,0,3}⇒Range of ...

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Standard XII

Mathematics

Domain

A Relation R ...

Question

A relation $R$ is defined in the set of integers as follows $(x, y) \in R$ if $x^{2} + y^{2} = 9$ . Which of the following is false?

$R = \{(0, 3), (0, - 3), (3, 0), (- 3, 0)\}$

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$D o m a i n o f R = \{- 3, 0, 3\}$

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$R a n g e o f R = \{- 3, 0, 3\}$

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$N o n e o f t h e a b o v e$

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Solution

The correct option is D
$N o n e o f t h e a b o v e$

Explanation for the correct option:
Given, $x^{2} + y^{2} = 9$ , $(x, y) \in R$
$\Rightarrow x = \sqrt{9 - y^{2}}$
Therefore, set of $R = \{(0, 3), (0, - 3), (3, 0), (- 3, 0)\}$
$\Rightarrow$ Domain of $R = \{- 3, 0, 3\}$
$\Rightarrow$ Range of $R = \{- 3, 0, 3\}$
Thus, all the options are True except D.
Hence, Option ‘D’ is Correct.

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Similar questions

Q. If R is a relation defined on the set Z of integers by the rule (x, y) ∈ R ⇔ x² + y² = 9, then write domain of R.

Q. If R = {(x, y) : x, y ∈ Z, x² + y² ≤ 4} is a relation defined on the set Z of integers, then write domain of R.

Determine whether each of the following relations are reflexive, symmetric and transitive:

(i)Relation R in the set A = {1, 2, 3…13, 14} defined as

R = {(x, y): 3x − y = 0}

(ii) Relation R in the set N of natural numbers defined as

R = {(x, y): y = x + 5 and x < 4}

(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} as

R = {(x, y): y is divisible by x}

(iv) Relation R in the set Z of all integers defined as

R = {(x, y): x − y is as integer}

(v) Relation R in the set A of human beings in a town at a particular time given by

(a) R = {(x, y): x and y work at the same place}

(b) R = {(x, y): x and y live in the same locality}

(d) R = {(x, y): x is wife of y}

(e) R = {(x, y): x is father of y}

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.

Q. A relation

R

from set

A = {1, 2, 3, 5}

B = {1, 4, 9, 15}

is defined as :

R = {(x, y) : x = \sqrt{y}; x \in A, y \in B},

then which of the following option is correct ?

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A relation R is defined in the set of integers as follows (x,y)∈R if x2+y2=9. Which of the following is false?

The correct option is D NoneoftheaboveExplanation for the correct option:Given, x2+y2=9, (x,y)∈R⇒x=9–y2Therefore, set of R=(0,3),(0,-3),(3,0),(-3,0)⇒Domain of R=-3,0,3⇒Range of R=-3,0,3Thus, all the options are True except D.Hence, Option ‘D’ is Correct.

A relation $R$ is defined in the set of integers as follows $(x, y) \in R$ if $x^{2} + y^{2} = 9$ . Which of the following is false?