Is P ^ ¬(Q ^ R) in DNF?

Question

¬(Q ^ R) can be (¬Q v ¬R) according to De Morgan’s Law

So we get P ^ ¬Q v ¬R which can be written as

(P ^ ¬Q) v (¬R) which is in DNF

So can I say that P ^ ¬(Q ^ R) is in DNF?

Answer 1

Every formula can be converted to DNF, but the fact that a formula can be converted to DNF does not imply that that formula is DNF itself

So, (P ^ ¬(Q ^ R)) is not DNF, but ((P ^ ¬Q) v (P ^ ¬R)) is DNF

Answer 2

DNF (and CNF, and NNF, and ..) are about the syntactical nature of the expression. Once you start rewriting the expression into a different one, even if it is logically (i.e semantically) equivalent, it is no longer that same syntactical expression. So, just because the logical equivalent of some statement is in DNF does not mean that the original is in DNF.