Left half plane:

<UL>
   <LI>$
      A_1=
      \left\{
         (x,y) \in \mathbb{R}^2
         |~
         x \leq 0 \wedge y \gt mx+k
      \right\}
   $</LI>
   <LI>$
      A_2=
      \left\{
         (x,y) \in \mathbb{R}^2
         |~
         x \leq 0 \wedge y \lt mx+k
      \right\}
   $</LI>
</UL>