(A)$(x, y) \in R \Leftrightarrow 0 < |x| - |y| \le 1$ is neither transitive nor symmetric.
(B)$(x, y) \in R \Leftrightarrow 0 < |x - y| \le 1$ is symmetric and transitive.
(C)$(x, y) \in R \Leftrightarrow |x| - |y| \le 1$ is reflexive but not symmetric.
(D)$(x, y) \in R \Leftrightarrow |x - y| \le 1$ is reflexive and symmetric.