Question

Reduce the following Boolean expression(Simplify using Boolean laws):- a) (X +Y) ( X+ Y’ ) ( X’ +Z) b) (X +Y) ( X+ Y’ ) ( X’ +Z)

Answer 1

a)      And   b)  both are same

a) (X +Y) ( X+ Y’ ) ( X’ +Z) = (X+XY’+XY+YY’)( X’ +Z)

= (X+X(Y’+Y)+YY’)( X’ +Z)         Since YY’ = 0 and  Y+Y’ = 1 Then

= ( X + X(1) + 0 ) )( X’ +Z)           Since X + X  = X Then

= X ( X’ + Z ) = XX’ +XZ               Since XX’ = 0 Then

= XZ

(X +Y) ( X+ Y’ ) ( X’ +Z)  = XZ