We're asked to find the minimum element of the set S, where $S={\{(0,2), (1,1), (1,2), (4,0)\}}$ , and the minimum element x with respect to K is defined s.t. $y \in S \iff x \preccurlyeq_k y$. The solution is given as (0,2).
Why is (0,2) the minimum element rather than (1,1), when 2 is greater than 1?