Define the Set of Alternatives X as
Define the weakly preferred relation on X as
$\succsim : X \to X$ such that $(\forall x \in X)(\forall y \in X)$ , it is the case that
$y \succsim x \iff x+y \leq 4$
The definition for completeness can be referred below:-
$(\forall x \in X) (\forall y \in X) [ x \neq y \Rightarrow x \succsim y \: \lor y \succsim x] \Rightarrow \: \succsim $ is complete
Clearly, we can find counter example to show that $\succsim$ is not complete.
Notice from the definition of $\succsim$, it also holds that
$\neg (y \succsim x) \iff \neg(x+y \leq 4)$
Counterexample can be, $\neg(3 \succsim 2)$ as $2+3 > 4$ and $\neg(2 \succsim 3) $ as $3+2>4$
Since $(\exists x \in X)(\exists y \in X) [x \neq y \land \neg (x \succsim y) \land \neg(y \succsim x)]$ is true ,which is negation of definiton of completeness, it can be concluded that $\succsim$ is not complete.