Boolean algebra - cube - minimal disjunctive normal form

Question

I have a test coming up and I would like to know how to solve these kinds of problems. This is the description:

Find MDNF (minimal disjunctive normal form) of the function F(A, B, C),
which is described by the cube. A full circle means logical 1, an empty
circle means logical 0.

How do I solve this in general?

Answer 1

The cube diagram can be translated into a sum of minterm expression:

(a and b and !c) or (!a and b and !c) or (a and !b and c) or (!a and !b and c)

This can be depicted as Karnaugh map to visualize that the four 3-literal terms can be merged into two 2-literal terms:

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

The minimal sum of minterms:

(!b and c) or (b and !c)        [corresponds to mutiple-choice answer (d)]

The minimal product of maxterms:

(b or c) and (!b or !c)