Which form of the function is simpler?

Question

I'm simplifying function in Boolean algebra. Which form is simpler:

$AB' + C'D + A'BC$

OR

$DA' + C'D + AB'$

Second form has less letters but overlays itself at more spots. Which one is simpler?

Answer 1

The two functions are similar but not equivalent:

a!b + !cd + !abc

             ab
       00  01  11  10
      +---+---+---+---+
   00 | 0 | 0 | 0 | 1 |
      +---+---+---+---+
   01 | 1 | 1 | 1 | 1 |
cd    +---+---+---+---+
   11 | 0 | 1 | 0 | 1 |
      +---+---+---+---+
   10 | 0 | 1 | 0 | 1 |
      +---+---+---+---+

a!b + !ad + !cd

             ab
       00  01  11  10
      +---+---+---+---+
   00 | 0 | 0 | 0 | 1 |
      +---+---+---+---+
   01 | 1 | 1 | 1 | 1 |
cd    +---+---+---+---+
   11 | 1 | 1 | 0 | 1 |
      +---+---+---+---+
   10 | 0 | 0 | 0 | 1 |
      +---+---+---+---+

The second function is simpler, because its sum of products consists of three conjunctions with two literals each. The first function consists of two conjunctions with two literals each and a third conjunction with three literals. This third conjunction is thus one literal "heavier".