Complementary for $SAT$ I have tried to find a definition of complementary language to $SAT$, I mean $\overline{SAT}$.
But I still confused, in case of $L\in \overline{SAT}$ is it mean:
if $\varphi\in L$ then all interpretations are satisfy and
if $\varphi\notin L$ then exists interpretation that unsatisfy
OR vice versa
if $\varphi\notin L$ then all interpretations are satisfy and
if $\varphi\in L$ then exists interpretation that unsatisfy
please if you downvote write explanation of why
Usually, when we talk about the complement of a set we have some reference set to compare to.
In the setting of languages over some alphabet $\Sigma$, this means that the complement of some language $L$ would be $\overline L = \Sigma^\ast \setminus L$, i.e. the set of all strings over $\Sigma$ which are not in $L$.
In the particular case of
$$\mathrm{Sat} = \{\langle \psi \rangle \in \Sigma^\ast \mid \langle \psi \rangle \text{ encodes a satisfiable propositional formula } \psi \}$$
we find that
$$\overline{\mathrm{Sat}} = \{w \in \Sigma^\ast \mid w \text{ does not encode a satisfiable propositional formula } \psi \}$$
and hence, $\overline{\mathrm{Sat}}$ consists of all strings which represent unsatisfiable propositional formulas (i.e. ones that have no satisfying interpretations) and all strings which don't represent formulas at all.