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Maths-

General

Easy

Question

For real numbers $x$ and $y comma$ we write $x blank R y left right double arrow x minus y plus square root of 2$ is an irrational number. Then, the relation $R$ is

(a) Reflexive
Symmetric
Transitive
None of these

The correct answer is: (a) Reflexive

For any $x element of R comma$ we have
$x minus x plus square root of 2 equals square root of 2$ an irrational number
$rightwards double arrow x blank R blank x$ for all $x$
So, $R$ is reflexive
$R$ is not symmetric, because $square root of 2 blank R blank 1$ but $1 square root of 2$
$R$ is not transitive also because $square root of 2 blank R blank 1$ and $1 blank R blank 2 blank square root of 2$ but $square root of 2$ $2 square root of 2$

Related Questions to study

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Consider the following statements:
i) Every reflexive relation is antisymmetric
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