What is a "non-relaxed" DNF is then? I would say, the requirement to have each variable in every conjunct makes it the most stringent DNF. This would probably make the derivation pretty long. If not every variable has to appear, then would work as a DNF."Relaxed" DNF means we must have disjunctions of conjunctions in which eachvstatement variable occurs exactly once
Your DNF is correct except that it misses r in the second disjunct. It is not necessary to write all the parentheses. In fact, more compact notations are preferable for DNFs, such as instead of .