The atomic propositional variables $p_0,p_1,...$ are $\textit{formulas},$ called $\textit{prime formulas},$ also called $\textit{atomic}$ formulas, or simply $\textit{primes}.$
Prime formulas and negations of prime formulas are called $\textit{literals.}$ A disjunction $\alpha_1 \vee \alpha_2 \vee...\vee \alpha_n,$ where each $\alpha_i$ is a conjunction of literals, is called a $\textit{disjunctive normal form},$ a $\textit{DNF}$ for short.
Similarly, A conjunction $\beta_1 \wedge \beta_2 \wedge...\wedge \beta_n,$ where each $\beta_i$ is a disjunction of literals, is called a $\textit{conjunctive normal form},$ a $\textit{CNF}$ for short.
Which of the following statement(s) is/are correct?
- $p \vee (\neg p \wedge q)$ is a DNF.
- $p \vee q$ is at once a DNF and a CNF
- $p \vee q \vee \neg (\neg p \wedge q)$ is neither a DNF nor a CNF.
- $p \vee \neg (\neg p \wedge q)$ is either a DNF or a CNF.