I am stuck on a particular problem. I need workout the sum of products and then plot as a k-map. I am confident of the k-map part once i have the sum of products.

(A + B' C)' + (A B + C')'

Any help please?

 

There are two ways to do it.

Method #1 Make a function table with three inputs, A, B, and C, and one output call it Y. Fill in the rows with 1's and the sum of products can be written by inspection.

  A  B  C |  Y
---------|---
  0  0  0  | 1
  0  0  1  | 1
  0  1  0  | 1
  0  1  1  | 1
  1  0  0  | 0
  1  0  1  | 1
  1  1  0  | 0
  1  1  1  | 0
 
A' + AB'C

Method #2 Algebraic manipulation using DeMorgans Law

(A + B'C)' + (AB + C')'
A'(B'C)'   + (AB)'C            DeMorgan's Law
A'(B + C') + (A' + B')C        Demorgan's Law -- again
A'B  +  A'C'  +  A'C  +  B'C   Distributive Rule
A'B  +  A'(C' +  C)   +  B'C   Distributive Rule and Identity Element
A'(B +  1)    + (A' + A)B'C    Identity Element
A'(B  + 1  + B'C)  + AB'C      Identity Element
A'  + AB'C