Find two pairs where neither is the case ⟨x1,y1⟩⪯⟨x2,y2⟩, ⟨x1,y1⟩⪰⟨x2,y2⟩.
Is $\le$ defined by $\langle 𝑥_1, 𝑦_1 \rangle \le \langle 𝑥_2, 𝑦_2 \rangle$, if $𝑥_1 \le 𝑥_2 \land𝑦_1 \ge 𝑦_2$ a linear order?