I want to bring the following formula $ F = A \land (A \lor B) \Rightarrow (B \lor C)$ into conjunctive normal form (CNF) and disjunctive normal form. Therefore, I applied the following 5 step transformation process:
- Step: Removing the implication:
$$ \Leftrightarrow \neg (A \land(A \lor B)) \lor (B \lor C)$$
Step: Resolve the negation: $$ \Leftrightarrow \neg A \lor (\neg A \land \neg B) \lor (B \lor C)$$
Step: Remove parenthesis to receive DNF $$ \Leftrightarrow \neg A \lor (\neg A \land \neg B) \lor B \lor C$$
Step: Resolve the absorption based on step 2: $$ \neg A \lor (B \lor C)$$
Step Removing parenthesis to have DNF as well as CNF: $$ \neg A \lor B \lor C$$
I just have three questions to my normal forms:
- Is this transformation process correct?
- Is the formula of step 3: $ \neg A \lor (\neg A \land \neg B) \lor B \lor C$ in DNF?
- Are DNF and CNF of step 5 correct? Is it necessary to remove the parenthesis for DNF and CNF?