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

For any x∈R, we have x-x+2=2 an irrational number.⇒xRx for all x. So, R is reflexive.R is not symmetric, because 2R1 but 1R2, R is not transitive also because 2R1 and 1R22 but 2R22.