Let A be the set of first ten natural numbers and let R be a relation on A- A defined by R-x-y - x-2y - 10-x-y- A- Then range of R-1 is

The correct option is A {2, 4, 6, 8}A = {1, 2, 3,...,10} x + 2y = 10 ⇒ y = 10 x2; x, y ∈ A_i ⇒ x = 2, 4, 6, 8 nbsp; ⇒ y = 4, 3, 2, 1 nbsp; nbsp; ∴ R= { ...

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Standard XI

Mathematics

Range

Let A be the ...

Question

Let $A$ be the set of first ten natural numbers and let $R$ be a relation on $A \times A$ defined by $R = {(x, y) : x + 2 y = 10; x, y \in A} .$ Then range of $R^{- 1}$ is

{2, 4, 6, 8}

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{1, 2, 3, 4}

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{1, 2, 4, 6}

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{1, 4, 6, 8}

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Solution

The correct option is A ${2, 4, 6, 8}$
$A = {1, 2, 3, . . ., 10}$
$x + 2 y = 10 \Rightarrow y = \frac{10 - x}{2}; x, y \in A_{i}$
$\Rightarrow x = 2, 4, 6, 8 \Rightarrow y = 4, 3, 2, 1$

$∴ R = {(2, 4), (4, 3), (6, 2) (8, 1)} \Rightarrow R^{- 1} = {(4, 2), (3, 4), (2, 6), (1, 8)}$

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Similar questions

Q. Let

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R = {(x, y) : x + 2 y = 10; x, y \in A} .

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Range

Standard XI Mathematics

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Let A be the set of first ten natural numbers and let R be a relation on A×A defined by R={(x,y):x+2y=10;x,y∈A}. Then range of R−1 is

The correct option is A {2,4,6,8}A={1,2,3,...,10} x+2y=10⇒y=10−x2;x,y∈Ai ⇒x=2,4,6,8⇒y=4,3,2,1 ∴R={(2,4),(4,3),(6,2)(8,1)}⇒R−1={(4,2),(3,4),(2,6),(1,8)}

Let $A$ be the set of first ten natural numbers and let $R$ be a relation on $A \times A$ defined by $R = {(x, y) : x + 2 y = 10; x, y \in A} .$ Then range of $R^{- 1}$ is

The correct option is A ${2, 4, 6, 8}$
$A = {1, 2, 3, . . ., 10}$
$x + 2 y = 10 \Rightarrow y = \frac{10 - x}{2}; x, y \in A_{i}$
$\Rightarrow x = 2, 4, 6, 8 \Rightarrow y = 4, 3, 2, 1$

$∴ R = {(2, 4), (4, 3), (6, 2) (8, 1)} \Rightarrow R^{- 1} = {(4, 2), (3, 4), (2, 6), (1, 8)}$