The correct option is B reflexive and symmetric
As (x,x) ϵ R ⇒ |x−x|≤ 1
⇒ 0 ≤ 1 (True),
Thus, reflexive.
As (x,y) ϵ R ⇒ |x−y|≤ 1
⇒ |y−x||≤1 ⇒ (y,x) ϵ R,
Thus, symmetric.
Again, (x, y) ϵ R and (y, z) ϵ R
⇒|x−y|≤ 1 and |y−z|1/⇒|x−z|≤ 1
∴ Not transitive