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

xRy⇔x−y+2 is an irrational number. Let (x,x)∈RThen, x−x+2=2which is an irrational number∴ xR×,∀x∈RR is an reflexive relation. R is not symmetric since 2,1∈R since 2-1+2 is irrational  but 1,2 ∉R since 1-2+2=1, which is rational R is not transitive because  (1,3)∈R,since  (1−3+2) is an irrational number                                    and (3,2)∈R,since (3-2+2)=3 is an irrational number. but  (1,2)∉R since (1−2+2)=1 is a rational number.∴R is not transitive relation.