If in the 3 CNF formula I were to replace the ANDs with ORs and ORs with ANDs would the problem still be NP complete?

Question

Let us consider the 3 CNF formula.

$$ (x_1 \vee x_2 \vee \neg x_3) \wedge (x_2 \vee x_4 \vee \neg x_1) \cdots $$

We know that finding a true value for the above expression, which consists of $m$ clauses and $n$ variables, is NP-complete.

Is the clause below NP-complete?

$$ (x_1 \wedge x_2 \wedge \neg x_3) \vee (x_2 \wedge x_4 \wedge \neg x_1) \cdots $$

Answer 1

What you get with the substitutions you describe is a DNF (disjunctive normal form) formula.

Satisfiability for DNF is not NP-complete. To satisfy the whole formula it is enough to satisfy one term. To satisfy one term, satisfy all the literals in it. This holds regardless of the number of literals in each term.

What is hard for DNF is proving tautology, which is coNP-complete.