For real numbers x and y , we write xRy ∈ x - y + √ 2 is an irrational number. Then relation R i

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1.Relation and Function

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For real numbers $x$ and $y$, we write $ xRy \in $ $x - y + \sqrt 2 $ is an irrational number. Then the relation $R$ is

A

Reflexive

B

Symmetric

C

Transitive

D

None of these

Solution

(a) For any $x \in R,$ we have $x – x + \sqrt 2 = \sqrt 2 $ an irrational number.

==> $xRx$ for all $x$. So, $R$ is reflexive.

$R$ is not symmetric, because $\sqrt 2 R1$ but $1\,\not R\,\sqrt 2 $, $R$ is not transitive also because

$\sqrt 2 R1$ and $1R2\sqrt 2 $ but $\sqrt 2 \,\not R\,2\sqrt 2 $.

Standard 12

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