For $a \in \mathbb{C}$, let $A = \{z \in \mathbb{C} : \text{Re}(a + z) > \text{Im}(\bar{a} + z)\}$ and $B = \{z \in \mathbb{C} : \text{Re}(a + z) < \text{Im}(a + z)\}$. Then among the two statements:

(S1): If $\text{Re}(a), \text{Im}(a) > 0$, then the set $A$ contains all the real numbers.

(S2): If $\text{Re}(a), \text{Im}(a) < 0$, then the set $B$ contains all the real numbers.