Question

1. Simplify the equations using boolean algebra and show work:

a. AB + (AC)’+ AB’C(AB+C)

b. W + W’X’ + W’XY +W’X’Y’Z

c. ABC’ + ABC + A’B’C + AB’C+ A’BC

Answer 1

a. 
AB + (AC)’+ AB’C(AB+C)
= AB + (A' + C')+ AB’C(AB+C)
= AB + (A' + C')+ AB’CAB+AB’CC
= AB + (A' + C')+ 0 + AB’CC
= AB + (A' + C')+ AB’CC
= AB + (A' + C')+ AB’C
= A(B+B'C) + A' + C'


b. 
W + W’X’ + W’XY +W’X’Y’Z
= W + W’X’(1+Y’Z) + W’XY
= W + W’X’(1) + W’XY
= W + W’X’ + W’XY
= W + W’(X’ + XY)

c. 
ABC’ + ABC + A’B’C + AB’C+ A’BC
= AB(C’ + C) + A’B’C + AB’C+ A’BC
= AB(1) + A’B’C + AB’C+ A’BC
= AB + A’B’C + AB’C+ A’BC
= AB + A’(B’+B)C + AB’C
= AB + A’(1)C + AB’C
= AB + A’C + AB’C
= A(B+B'C) + A’C