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The 3-SAT problem, i.e. the problem whether a given Boolean formula consisting of clauses of at most 3 literals is known to be NP-complete. Then it’s complement, i.e. whether such a formula is unsatisfiable, is coNP-complete, right?

Gorid
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Let $\mathcal{L} \subseteq\Sigma^*$ be some language. The complement of $\mathcal{L}$ is$$\mathcal{L}^c=\Sigma^*\setminus \ \mathcal{L}$$ The class $\textbf{co-NP}$ is the complexity class (set of languages) whose complement is in $\textbf{NP}$. Formally

$$\textbf{co-NP}=\{\mathcal{L} \mid \mathcal{L}^c\in \textbf{NP}\}.$$ According to this link, because $\text{3-SAT}\in \mathbf{NP}\text{-complete}$, then by $\text{3-UNSAT}$ being the complement of $\text{3-SAT}$, $\text{3-UNSAT} \in \textbf{co-NP}\text{-complete}$.

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ErroR
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