could someone please be so kind to answer this question and explain the answer? Which of the following formulas are in CNF?
- ¬(A∨B∨C)∧(A∨B)
- (A∧B∧C)∨(A∧B)
- (A∨B∨¬C)∧(A∨B)
- (A∧B∧¬C)∨(A∧B)
2026-03-25 06:05:28.1774418728
Which of the following formulas are in CNF (conjunctive normal form)?
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CNF is when a Boolean expression is written as a conjunction of clauses, where a clause is defined as a disjunction of literals. And... a literal is either a simple proposition or its negation. In other words, the expression must be a conjunction of disjunctions of some combination of the variables $p,q,r,...$ or their negations. Think of CNF as a chain of conjunctions (ANDs) that join chains of disjunctions (ORs) which join propositions or their negations. As a helpful mnemonic, CNF is conjunctions of disjunctions.
For example, the following is in CNF:
$(p \vee q) \wedge s \wedge (\neg a \vee b \vee \neg c) \wedge t \wedge \neg w$
Options 2 and 4 are disjunctions of conjunctions, so they are not in CNF. Option 1 seems to be a good candidate, but if you inspect it carefully you will notice there is a negation of a set of parentheses and not a simple proposition. If a negation is present, then it must be the negation of a simple proposition. If you were to apply DeMorgan's rule (by distributing the negation and changing the disjunctions in the parantheses to conjunctions), then 1 would be in CNF.
Option 3 is the only option composed of pure literals written in terms of conjunctions of disjunctions, so...
3 is in CNF.