Which of the following is not correct for relation \(R\) on the set of real numbers? [JEE Main 2021, 31 Aug (Shift 1)]

\((x, y) \in R \Leftrightarrow 0<|x|-|y| \leq 1\) is neither transitive nor symmetric.

\((x, y) \in R \Leftrightarrow|x-y| \leq 1\) is reflexive and symmetric.

\((x, y) \in R \Leftrightarrow|x|-|y| \leq 1\) is reflexive but not symmetric.

\((x, y) \in R \Leftrightarrow 0<|x-y| \leq 1\) is symmetric and transitive.