# Which of the following formulas are in CNF (conjunctive normal form)?

could someone please be so kind to answer this question and explain the answer? Which of the following formulas are in CNF?

1. ¬(A∨B∨C)∧(A∨B)
2. (A∧B∧C)∨(A∧B)
3. (A∨B∨¬C)∧(A∨B)
4. (A∧B∧¬C)∨(A∧B)
• $1$ and $3$ are in CNF, Since they connected with $\wedge$ – Manx Sep 24 '19 at 20:22
• @Manx Option 1 is not in CNF as there is a negation of the disjunction $A \vee B \vee C$. – RyRy the Fly Guy Sep 24 '19 at 21:16
• I see, thank you sir :) – Manx Sep 24 '19 at 22:12

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.
$$(p \vee q) \wedge s \wedge (\neg a \vee b \vee \neg c) \wedge t \wedge \neg w$$