Let $A, B ⊂ \mathbb{R}^n$ be two nonempty sets such that $A ∩ B = ∅$. $H(A, B) := \{(w, d) ∈ \mathbb{R}^{n+1} : \sup_{x\in A} \langle w,x\rangle ≤ d ≤ \inf_{y \in B} \langle w, y\rangle \}$
How do I find $H(A,B)$ explicitly for when
$A:=\{x_1,x_2\} \in \mathbb{R}^2 : x_1 \leq 0\}$
$B:= \{x_1,x_2\} \in \mathbb{R}^2: x_1 > 0 \}$