Define a function S : Z+ → Z+ as follows. For each positive integer n, S(n) = the sum of the positive divisors of n S(18)?
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Define a function S : Z+ → Z+
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- Define a function S : Z+ → Z+ as follows. For each positive integer n, S(n) = the sum of the positive divisors of n. Find S(17)Give an example of a function from Z to N that is one-to-one, but not onto.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.
- How do we define that a function f(n) has an upper bound g(n), i.e., f(n) ∈ O(g(n))?Simplify the following Boolean expressions, using four-variable K-maps: AB′C+B′C′D′+BCD+ACD′+A′B′C+A′BC′DThe 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…
- Simplify the following Boolean expressions, using four-variable K-maps: x′z+w′xy′+w(x′y+xy′)Simplify Boolean function using K map. Variables are marked in a,b,c,d order 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 Question 37 options: ac’ + ad + bd + a’c ac’ + bd’ + a’c ac’ + bd + a’c None of above c’a + b’c’ + abLet f be a function from the set of length 10 binary numbers to the set of subsets of A={1, 2, ...,10 } given by f(b1,b2...b10)={i in A|bi=1}. Determine f^-1({1,3,5,6})
- Affine transformations preserve parallel lines. True or falseSimplify the following Boolean functions by means of K-map:a) f(A,B,C) =∑m(0,2,3,4,6)b) f(A,B,C,D) = ∑ m(0,2,3,7,8,10,12,13)c) F(X,Y,Z) = Y’Z+YZ+X’Y’Z’Implement boolean function f(A, B, C, D) =( 0,2,5,8,10, 14) B part :(A, B, C, D) =(2, 6,11)