I want to find the negation of a CNF expression which is also in CNF form.
How do I do that? Do I do the negation into DNF and then convert that DNF to CNF?
2026-03-25 19:05:13.1774465513
Finding the negation of a formula in CNF that is also in CNF
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Do a bunch of DeMorgan's, Double Negations, and Distributions.
The DeMorgans and Double Negations will get it into DNF.
The Distributions will get it into CNF.
Example:
CNF formula:
$$(A \lor \neg B) \land (\neg C \lor D)$$
Negated:
$$\neg((A \lor \neg B) \land (\neg C \lor D))$$
DeMorgans:
$$\neg (A \lor \neg B) \lor \neg (\neg C \lor D))$$
More DeMorgans:
$$(\neg A \land \neg \neg B) \lor (\neg \neg C \land \neg D))$$
Double Negations:
$$(\neg A \land B) \lor (C \land \neg D))$$ (now it is in DNF)
Distribution:
$$((\neg A \land B) \lor C) \land ((\neg A \land B) \lor \neg D))$$
More Distributions:
$$(\neg A \lor C) \land (B \lor C) \land (\neg A \lor \neg D) \land (B \lor \neg D)$$
CNF!