Hardware & Architecture HW #5-100 Pts 1. (25 Pts - 5 Pts Each) Reduce the following expressions using Boolean Algebra a) A+ ABC + AB b) ABC + ABC + C c) ABC + ABC + ABC d) AC + AB+ AB e) (A + B)C + (CD) + B 2. (6 Pts) Prove that AB + B = A + B using a truth table. Input combinations must be sequential. A B B AB AB + B A+ B Explain how this proves the relationship.

please help me solve ! boolean algebra

Simplify these  two given Boolean expressions1. AB+AB’2. (A+B)(A+B’)

71 Use the Boolean algebra to: a. Prove that: x (x. y) + x (x +y) + (x. y)) = x ỹ %3D b. Solve the expression: F(x,y,z) = xy Z + xyz+xy z %3D c. Solve the expression: F(A, B, C) = A BC+ABC+AB C+A BC

14. Simplify the following functional expressions using Boolean algebra and its identities. List the identity used at each step. 1. a) F(x, y, z) = y(x' + (x+y)')

Find the complement of the following Boolean functions, and provide their final simplified functions if possible: (a) x'y'z' + xyz. (b) x'y+xz' + yz (c) bc + a'c' (d) x'y + xy' (e) x(y'z' + yz) (f) y'z(xw+y'w')