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