$R$ is the relation on $\mathbb{Z}$ given by $a \mathrel{R} b$ if $ab \ge 0$. Which of these describes $R$?

Explanation

1. 01

   $a \cdot a = a^{2} \ge 0$, and $ab = ba$, so it is reflexive and symmetric.

2. 02

   $(-1)(0) \ge 0$ and $(0)(1) \ge 0$, but $(-1)(1) < 0$: not transitive.