Derivation using Logical Laws
Let A be the statement form . Find a statement form B in "relaxed" disjunctive normal form which is logically equivalent to A. Then Show that (i.e. derive B from A using logical laws).
Here's my truth table, I've marked with a * the rows where A is true:
So the disjunctive normal form would be:
Is this correct? ("Relaxed" DNF means we must have disjunctions of conjunctions in which eachvstatement variable occurs exactly once).
Now, we must derive B from A using logical laws
(De Morgan's law)
This is how far I've got. Could anyone please show me how to complete this?
P.S. Here are the list of all laws http://img833.imageshack.us/img833/9242/laws.jpg
Re: Derivation using Logical Laws
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 .