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1.Relation and Function
hard
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
Mathematics
