Question

The simplification of the Boolean expression (ABC)+(ABC)
(CR 8marks)
(

The function is (A'BC') '+(AB' C) '

Answer 1

1) Given Boolean expression F = (ABC)+(ABC)

F = (ABC)+(ABC)

F = (ABC)

Which is Required Simplified Boolean expression

2) Given function is (A'BC')'+(AB'C)'

F = (A'BC')'+(AB'C)'

F = [(A')'+B'+(C')'] + [A'+(B')'+C'] { We know that (PQ)'= P' + Q' }

F = [A+B'+C] + [A'+B+C']  { We know that (P')'= P }

F = A+B'+C+(A'+B)+C'

F = A+(A'+B)+B'+C+C' {Commutative law (P + Q) = (Q + P)}

F = (A+A')+(B+B')+(C+C')  {Associative law (P + Q) + R = P+ (Q + R)}

F = (1)+(1)+(1)  { We know that P+P'= 1 }

F = (1) { We know that 1+1+1= 1 }

F = 1

Which is Required Simplified Boolean expression