Using the Definitional proof, show that each of these functions is O(2²). (a) f(x)= 5x (b) f(x)= 5x +5 (c) f(x)= 5x² + 5x +5 (d) f(x)= 5x² + 5log(x)

1. Consider the following functions of n. (1) (2) (3) (4) (5) (6) (7) (8) (9) fi(n) = n, if n = 2.k for k = 0, 1, 2,... = n², otherwise. f2(n) = n, if n = 3.k for k= 0, 1, 2,... = n², otherwise. f3(n) = log n. Answer the following questions and prove your answ Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. Yes or No. fi(n) = 2(f₂(n)), f2(n) = Q(fi(n)), fi(n) = 0 (f₂(n)), f₂(n) = 0 (fi(n)), fi(n) = O(n), f₂(n) = O(n²), f3(n) = O(√n), f3(n) = O(fi(n)), 22n = 0(2¹), swer for each one.

Please use four variables K-map and show your work on a paper

1. Simplify the following Boolean functions, using four-variable maps: (a) F1(w,x,y,z) = E(1, 4, 5, 6, 12, 14, 15) (b) F2(A,B,C,D) = [(0,1,2,4,5,7,11,15) (c) F3(W,x,y,z) = II(0,1,4,5,6,7,8,9)

Express the following functions as sum of minterms and product of maxterms: (a) F(A, B, C, D) = BD+ AD+ BD (b) F(x, y, z) = (xy +z)(xz + y) %3D

Simplify the following Boolean functions using four-variable maps. PLEASE EXPLAIN IN WRITING THE STEPS AND WHAT IS GOINING ON F(A, B, C, D) =∑ (4, 6, 7, 15) F(A, B, C,D) =∑ (0, 2, 4, 5, 6, 7, 8, 10, 13, 15)

need help simplifying equation