Converting $\lnot a \land \lnot b$ to CNF

Question

I tried as much as I could. I tried adding a double negation in front, which led to $$ \lnot a \land \lnot b=\lnot (a \lor b) $$ I also tried to "and" with the same formula again but I got no result. Is there some general procedure for converting between CNF and DNF?

Answer 1

It's both in conjunctive and disjunctive normal form. However the terms/factors are different. To make it more clear in conjunctive normal form it's

$$(\neg a) \land (\neg b)$$

and in disjunctive normal form it's

$$(\neg a \land \neg b)$$

Where the factors/terms are inside the parenthesis (in the later there's only one term which make the $\lor$ sign absent). If the terms/factors are only literals or their negation (that is there's apart from literal and negated literals only $\lor$s or only $\land$s) it's in both DNT and CNT.

Note that the normal forms does not require the expression to be minimal in any sense (which isn't guaranteed to be unique anyway). So there may be many solutions to the problem.

Answer 2

It's already in conjunctive normal form.