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

$\left(x,y\right)\in R\iff 0<\left|x\right|-\left|y\right|\le 1$ is neither transitive nor symmetric.

$\left(x,y\right)\in R\iff <\left|x-y\right|\le 1$  is reflexive and symmetric.

$\left(x,y\right)\in R\iff <\left|x\right|-\left|y\right|\le 1$  is reflexive but not symmetric.

$\left(x,y\right)\in R\iff 0<\left|x-y\right|\le 1$ is symmetric and transitive.