For $a \in \mathbb{C}$, let $A = \{\, z \in \mathbb{C} : \Re(a + \bar z) > \Im(\bar a + z) \,\}$ and $B = \{\, z \in \mathbb{C} : \Re(a + \bar z) < \Im(\bar a + z) \,\}$. Then among the two statements: (S1): If $\Re(a), \Im(a) > 0$, then the set $A$ contains all the real numbers. (S2): If $\Re(a), \Im(a) < 0$, then the set $B$ contains all the real numbers.