I have a proposition logic knowledge base which contains my neg query in CNF: $$\begin{split}1.~& \neg P \lor Q\\ 3.~& P \\ 4.~& R \lor S\\ 5.~& \neg R\end{split}$$
Is it possible to transfer them into set theory? Are all these syntacitally and semantically correct?
$$ K =\{(\neg P \lor Q), (P), (R \lor S), (\neg R) \}$$ $$ K =\{\{\neg P \lor Q\}, \{P\}, \{R \lor S\}, \{\neg R\} \}$$ $$ K =\{\{\neg P , Q\}, \{P\}, \{R , S\}, \{\neg R\} \}$$
All are valid representations of a CNF, depending on the task.
The first is a set of predicates, which so happen to all be disjunctions or literals. When the set is read conjunctively, this is a CNF.
The second is a set of clauses, several of which have terms which are disunctions rather than literals or negated literals. This is ... not wrong, but rarely used as is.
The third is a set of clauses, each of which are sets of literals or negations of literals. This is the preferred representation when the task is resolution.