How to convert to Disjunctive Normal Form

Question

The question gives the following: ¬(p ∨ ¬q) → (¬r ∧ (p → r))

With my own working, I have come to the answer of (p ∨ ¬q) ∧ (¬r ∧ ¬p) ∧ (¬r ∧ r). Can anyone tell me if this is correct?

Also, please tell me what Disjunctive Normal Form really means (without complicated terminology). The answer I got was from trying to break down what other similar questions have done. I still don't know what it really means.

Answer 1

As said in the comments, Wikipedia is indeed a good source for simple explanation. It also includes examples and counter-examples of formulas that are and are not in DNF, respectively.

Taken from the Wikipedia article, a formula is in DNF iff it is

a disjunction of conjunctions; it can also be described as an OR of ANDs

An OR of ANDs means that ORs can appear only outside of parentheses and ANDs can appear only inside. In your formula, there are several ANDs outside the parentheses and one OR inside the first parntheses, so that's why your formula is not in DNF.

Let's not forget that part of the definition of a DNF is that negation ($\neg$) can appear only in front of variables ($p, q, r$) and not outside of parentheses.