Ex 1 simplify

Z = A'BC+A'

A'(BC+1)=A'

EX 2

Z=[X+Y][X+Y']

=X+XY'+YX+YY'

=X[1+Y+Y']=X

Suppose X = A+B'C then

Z=[A+B'C+Y][A+B'C+Y']

and if Y = D+EF then

Z=[A+B'C+D+EF][A+B'C+(D+EF)']

which could be expanded by hand to obtain

Z=A+B'C

Ex 3 simplify

Z=(AB+C)(B'D+C'E)+(AB+C)'

LET X=B'D+C'E, Y=(A+BC)'

Y'X+Y=X+Y=B'D+C'E+(A+BC)'

SINCE, BY 2-14D XY'+Y=X+Y