Create K-maps and then simplify for the following functions 2) F(x, y, z) = yz’ + x’y + z’

The question describes a function S(k) which is defined as the sum of the positive divisors of a positive integer k, minus k itself. The function S(1) is defined as 1, and for any positive integer k greater than 1, S(k) is calculated as S(k) = σ(k) - k, where σ(k) is the sum of all positive divisors of k. Some examples of S(k) are given: S(1) = 1 S(2) = 1 S(3) = 1 S(4) = 3 S(5) = 1 S(6) = 6 S(7) = 1 S(8) = 7 S(9) = 4 The question then introduces a recursive sequence a_n with the following rules: a_1 = 12 For n ≥ 2, a_n = S(a_(n-1)) Part (a) of the question asks to calculate the values of a_2, a_3, a_4, a_5, a_6, a_7, and a_8 for the sequence. Part (b) modifies the sequence to start with a_1 = k, where k is any positive integer, and the same recursion formula applies: for n ≥ 2, a_n = S(a_(n-1)). The question notes that for many choices of k, the sequence a_n will eventually reach and remain at 1, but this is not always the case. It asks to find, with an explanation, two specific…

Given g = {(1,c),(2,a),(3,d)}, a function from X = {1,2,3} to Y = {a,b,c,d}, and f = {(a,r),(b,p),(c,δ),(d,r)}, a function from Y to Z = {p, β, r, δ}, write f o g as a set of ordered pairs.

Simplify the following two Boolean functions using K-MAP:c) F(A, B, X, D) = ∑ (2, 3, 10, 11, 12, 13, 14, 15) d) F(A, B, C, D) = ∑ (0, 2, 4, 5, 6, 7, 8, 10, 13, 15)

Simplify the following functions using K-maps, and then derive the corresponding simplified Boolean expressions. Note that d stands for don't-care cases. a) F(x, y, z) = (0,2,4,5) b) F(x, y, z) = (0,1,2,3,5) c) F(x, y, z) = Σ(1,2,3,6,7) d) F(x, y, z) = Σ(3,4,5,6,7) e) F(A,B,C,D) = Σ(4,6,7,15) f) F(w, x, y, z) = Σ(0,2,8,10, 12, 13, 14) g) F(w, x, y, z) = Σ(0, 2, 3, 5, 7, 8, 10, 11, 14, 15) h) F(A, B, C, D) = [(1,3,6,9,11,12,14) i) F(x, y, z) = Σ(0,4,5,6) and d(x, y, z) = Σ(2,3,7)

Determine whether each of these functions is a bijection from ℝ to ℝ. If it is, write the inverse function. f(x) = 2x3-5

1. Find the minimum sum of products and product of sums expressions for both of the following functions using K-Maps?(????) = ∑ ?(5,6,7,8,9,13,14) + ?(3,4,11,12)F(WXYZ)= XYZ’ + WX’Z + W’XYZ +WXY + WX + W’YZ’

6. X is (a,b,c,d), Y is {1,2,3,4). {(a,1), (b,2), (c,2), (d,4)) is a function from X to Y.

f(x) = -1.26 – 1.5x + x2 Find the root of the function by using one of the open methods or bracket methods with relative errors ea smaller than the maximum relative error ea = 0.001% (using matlab)

Can you represent the following Boolean function f(A, B) with a linear classifier? If yes, show the linear classifier. If not, briefly explain why not. f(A, B) A B 1 1 1 1