2.3 Simplify each of the following expressions by applying one of the theorems. State

the theorem used.

(a) X'Y'Z + (X'Y'Z)'

(c) ACF + AC'F

(e) (A'B + C + D)(A'B + D)

(b) (AB' + CD) (B'E + CD)

(d) A(C+ D'B) + A'

(f) (A + BC) + (DE + F)(A + BC)'