Karnaugh Map result = Using principles ?

Question

Does using Karnaugh Map produce same result as using principles to simplify boolean expression?

Answer 1

It depends on what the goal is as far as 'simplifying' goes. The Karnaugh map will produce either a statement in DNF (if you focus on the 1's or True's), or CNF (if you focus on the 0's or False's), and often that is the goal of the simplification. But sometimes this statement can be further 'simplified' (e.g in terms of the number of connectives, or length of statement) using algebraic principles. Also, if you have connectives like $\rightarrow$ or XOR, you can sometimes get a much simpler statement than that you get with the Karnaugh map. For example, see what you get from the Karnaugh map if you consider the statement $P \: XOR \: Q \: XOR \: R$!