Problem 1 Simplify the following equations into their minimal sum-of-products form using Boolean algebra. Every step annotated with a postulate or theorem. b. ab +c. (c + cd) : given Problem 2 Minimize the Boolean equations represented by the following equations switching equations. Postulates and theorems of intermediate steps are required. 1. f(a,b,c) = m(0,1,5,7) (into minimum SOP form) 2. f(a,b,c,d) = m(0,1,10,11,15) (into minimum SOP form) 3. f(a,b,c,d) = |M(2,3,6,7,10,11,14,15) (into minimum POS form) 4. f(a,b,c,d) = m(2,3,6,7,8,9,12,13) (into minimum SOP form) P2 P3 P4 Expression a +0 = a a + b = b + a a + (b + c) = (a + b)+c a + bc = (a + b)(a + c) a t= 1 a ta = a a +1=1 Dual a:1= a ab = ba a(bc) = (ab)c a(b + c = ab + ac a. = 0 a.a = a a. 0 = 0 P5 P6 T1 T2 T3 T4 T5 T6 T7 a + ab = a a(a + b) = a a + ab = a + b al + b) = ab ab + ab = a (a + b)(a + b = a ab + abc = ab + ac (a + b)(a +b+c) = (a + b)(a + c) a+b = b ab = a + ] ab +c + bc = ab +c (a + b) ( + c)(b + c) = (a + b)( + c) f(x1,x2,...,xn) = x1(f(1,x2,...,xn) + Xif(0, X2, ...,xn) f(x1,x2,...,xn) = [X1 + f(0, X2,...,xn)][X1 + f(1,x2,...,xn)] T8 T9 T10(a) T10(b)