JEE Mains Model Paper 25

x ∊ R ⇒ x - x + √5 = √5 is an irrational number
∴ (x, x) ∊ R , so R is reflexive
(√5 , 1) ∊ R because , √5 - 1 + √5 = 2√5 - 1 which is an irrational number
Also, (1, √5) ∊ R if 1 - √5 + √5 = 1 , which is not an irrational number
∴ (1, √5) ∉ R
∴ R is not symmetric
We have (√5 , 1) , (1 , 2√5) ∊ R because
√5 - 1 + √5 = 2 √5 and 1 - 2√5 + √5 = 1 - √5 are irrational numbers
Also (√5 , 2√5) ∉ R . So, R is not transitive