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GO Classes DPP | GATE CS | Discrete Mathematics| Set Theory

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Which of the following is not correct for relation $R$ on the set of real numbers?

  1. $(x, y) \in R \Leftrightarrow 0<|x|-|y| \leq 1$ is neither transitive nor symmetric.
  2. $(x, y) \in R \Leftrightarrow 0<|x-y| \leq 1$ is symmetric and transitive.
  3. $(x, y) \in R \Leftrightarrow|x|-|y| \leq 1$ is reflexive but not symmetric.
  4. $(x, y) \in R \Leftrightarrow|x-y| \leq 1$ is reflexive and symmetric.

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