2.11. (a) (d) Obtain the simplified expressions in sum of products for the following Boolean functions- xy + xyz + xyz AB+BC+BC (b) ab + bc + abc (e) D(A+B) + B (C + AD) (c) klm + kmn + klmn + lm (a) f(x, y, z) =m (2,3,6,7) (b) f(A,B,C,D) m (4,6,7,15) 2.12. Obtain the simplified expressions in sum of products for the following Boolean functions- 2.13. Obtain the simplified expressions in POS- (c) (d) f(A,B,C,D) m (7,13,14,15) f(w, x, y, z) =m (2,3,12,13,14,15) (a) f(x, y, z) =M (0,1,4,5) (b) f(a, b, c,d) M (0,1,2,3,4,10,11) (c) f(w,x,y,z) = M (1,3,5,7,13,15) 2.14. Simplify the following Boolean function by means of the tabulation method- (a) (b) (c) f=m (0,1,4,5,6,7,8,12,13) fm (1,3,5,7,13,15) and d = m (0,2,6) f = IIM (0,1,2,3,5,6,10,11) and d = [IM (13,14,15) where d is don't care condition.