Question

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

• A. Reflexive
• B. Symmetric
• C. Transitive
• D. None of these

Answer 1

Answer: (A)

Reflexive

Answer 2

For any $x \in R$ we have $x - x + \sqrt { 2 } = \sqrt { 2 }$ an irrational number.

⇒ $x R x$ for all x. So, R is reflexive.

R is not symmetric, because $\sqrt { 2 } R 1$ but $1 R \sqrt { 2 }$, R is not transitive also because $\sqrt { 2 }$ R 1 and $1 R 2 \sqrt { 2 }$ but $\sqrt { 2 } R 2 \sqrt { 2 }$ .