What are Different forms of a DNF (Disjunctive Normal Form)?

Question

I've read somewhere that there are many forms of DNF (Disjunctive Normal Form) for each statement. Can you give me an example? For example given the statement: p.q + ~p.r (which is in DNF) what other DNF forms are possible to write for this statement? Thank you!

Answer 1

Three Karnaugh maps show three ways to represent your expression

The maps demonstrate how the four minterms can be covered or grouped in terms with fewer variables:

$$qr \lor pq\bar{r} \lor \bar{p}\bar{q}r$$

$$pq \lor \bar{p}r$$

$$pqr \lor pq\bar{r} \lor \bar{p}\bar{q}r \lor \bar{p}qr$$

Each of these forms is a DNF, also called "sum of products".