Originally Posted by

**brooks972** I know that the disjunctive normal form is not unique.

<Start of excerpt from Wolfram MathWorld>

A statement is in disjunctive normal form if it is a disjunction (sequence of ORs) consisting of one or more disjuncts, each of which is a conjunction (AND) of one or more literals (i.e., statement letters and negations of statement letters; Mendelson 1997, p. 30). Disjunctive normal form is not unique.

<End of excerpt from Wolfram MathWorld>

For my purposes, I repeat, for emphasis, one sentence from the above excerpt:

Disjunctive normal form is not unique

OK.

( I use "~" to denote Logical-Negation, "+" to denote Logical-OR (inclusive), and "*" to denote Logical-AND )

I am _not_ looking for a formal proof of what I trying to do below; informality is sought.

I have a statement in conjunctive normal form, and I can express that statement in disjunctive normal form.

(~P + Q) * (P + ~Q) (Conjunctive Normal Form)

Using the Law of Distribution, this statement can be converted to

(~P * P) + (~P * ~Q) + (Q * P) + (Q * ~Q)

Because of the Law of Contradiction, this statement can be converted to

FALSE + (~P * ~Q) + (Q * P) + FALSE

which can be converted to

(~P * ~Q) + (Q * P) (which is in disjunctive normal form)

I want to arrive at another, logically equivalent, statement in disjunctive normal form :

(P * ~Q) + (~P * Q)

How do I get, informally,

From: (~P * ~Q) + (Q * P)

To: (P * ~Q) + (~P * Q)