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