Question

Simplify the following boolean algebraic equation
________ ________
Y=A.B'(A+C)+A'.B(A+B'+C')

Answer 1

you can simplify it by using k-map.

Answer 2

Y=A.B'(A+C)+A'.B(A+B'+C')
=(AB'+AB'C)+(A'AB+A'BB'+A'BC')
=AB'(1+C)+A'BC'
=AB'+A'BC'
=AB'+A'BC'
Let V=AB' and W=A'BC'
Y=V+W=((V+W)')' (Double Negation)

Using DeMorgan's Theorems
(M+N)'=M'.N'
(M.N)'=(M+N)'

Y=(V'.W' )'
=((AB')'.(A'BC')')'
=((A'+B).(A+B'+C))'
=(A'A+A'B'+A'C+AB+BB'+BC)'
=(A'B'+A'C+AB+BC)'
=(P+Q+R+S)'
=P'Q'R'S'
=(A+B).(A+C').(A'+B).(B'+C')
=(A+AB+AC').(A'B'+A'C'+BB'+BC')
=(A+AC').(A'B'+A'C'+BC')
=C'.(A'B'+A'C'+BC')
=(A'B'C'+A'C')+BC'
=A'C'(B'+1)+BC'
=A'C'+BC'
=C'(A'+B)

Answer 3

Sorry I did a mistake.
Y =(A+AC').(A'B'+A'C'+BC')
=A.(A'B'+A'C'+BC') >>A Instead of C'
=AA'B'+AA'C'+ABC'
=ABC'