4. Using DeMorgan's theorem simplify the following expression: (a' + bc')'

Answer the following questions: a. Apply DeMorgan's Theorems to the following expression F = (ABC + DEF)' b. Apply DeMorgan's Theorems to the following expression F = ((A+B+C). D)' c. Use DeMorgan's Theorem in algebraic form to Prove F = A' + B' (A. B)' d. Use DeMorgan's Theorem in algebraic form to Prove F = A'. B' = (A + B)' e. Minimize the following Logic Expressions F, Y Algebraically and PROVE the function F to be equal to A'.C' + B, and the function Y to be equal to A+BC. A'.B'.C + A'.B.C'+A'.B.C+A.B.C'+A.B.C F (A, B, C) Y (A, B, C) (A+B) (A+C)

Problem_#06] Using the truth table below, develop a simplified SOP expression using a Karnaugh Map. Inputs Output ABC X 1 000 001 010 011 100 101 110 1 0 1

Compute the following values of ψ(X, B), the number of B-smooth numbers between 2 and X. (c) ψ(50, 7)

3. Use the Karnaugh-Map to simplify the following expressions F(A, B, C) = ABC + ABC + ABC + ABC + ABC F(A,B,C,D) = A + AB + ABC + BCD + ACD ii.

2. (a) Compute and simplify f = (xz+ (y+t)' + (xz)'y')' Encircle final answer! (b) Prove or disprove that in any Boolean algebra, B: (i) 0' = 1 (ii) 1' = 0