Question

For real numbers x and y, we write xRy ⇒ x – y + √2 is an irrational number. Then the relation R is

1) Reflexive

2) Symmetric

3) Transitive

4) None of these

Answer 1

For each value of x ∈ R, x − x + √2 that is √2 is an irrational number.

It is reflexive.

Let x = √2 and y =2 then x − y + √2 = 2√2 – 2 which is irrational but when y = √2 and x = 2, x − y = √2 is not irrational.

It is not symmetric.

Let x − y + √2 is irrational & y − z + √2 is irrational then in above case let x = 1; y = √2 × 2 & z = 2

Hence x − z + √2 is not irrational, so, the relation is not transitive.