Find: f(f(f(14)), given the following definition: [FF(x- 2) – 2) f(x)= - (x+1 if x212 if x<12 O 8 10 O 11 O 14
Q: The following algorithm find the solution of a system of linear equations y using Gauss Elimination.…
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Q: Simplify the following equation 2 points Y=E(12, 8, 2, 6,10,5,7,) With d (0,4,14) O D'+A'C O D'+A'D
A: 1.
Q: Let A be the language defined as follows: A ={ xe{0,1}* | the number of Os in x is 4k+1 or 4k+2 for…
A: Regular expression of the given language
Q: Let g(n) = 13 + g(n) = 0(n4) giving the constants. + 23 + + n3. Show that %3D
A: According to principle methemetical induction 13 + 23 + 33 + … + n3 = (n(n+1)2)2 On Solving this we…
Q: Ql: prove using algebraic method that ABC + ĀBC + ABC + ABC = C Q2: Draw the circuit of the…
A: 1.) Algebraic Method
Q: Let A be the language defined as follows: A ={ xe{0,1}* | the number of Os in x is 4k+1 or 4k+2 for…
A: Regular expression of the given language
Q: f(n) such that f(n) ∈ O(n √ n) and f(n) ∈ Ω(n log n)) but f(n) ∈/ Θ(n √ n) and f(n) ∈/ Θ(n log n)).…
A: We know, big oh O, big Ω and big theta Θ notations are used to describe asymptotic upper bound,…
Q: f(x) is O(g(x)) if and only if g(x) is Ω(f(x)).
A: Proof: given: f:R---->R g:R----->R f(x) is O(g(x)) so we can say |f(x)|≤c|g(x)|.........(1)…
Q: Q9/ The minimum sum- of- products for the following function isF(A,B,C,D,E)=[m(0,1,15,16,17)…
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Q: Using the Definitional proof, show that each of these functions is O(2²). (a) f(x)= 5x (b) f(x)= 5x…
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Q: Simplify the following Boolean functions. F(w, x. y, 2) - !w!xly!z + !w!xy!z + !wx!y!z + !wxy!z +…
A: Here is the answer:-
Q: 27. Simplify the following Boolean expression A'.B.C'.D' + A'.B'.C.D + A'.B'.C.D +A.B.C.D+A'.B.C.D'+…
A: Given Boolean expression is, Y=A'BC'D'+A'B'C'D+A'B'CD+A'BCD+A'BCD'+AB'C'D+AB'CD Y=∑(4,1,3,7,6,9,11)…
Q: the result is T=3;C=3;x=5;z=0%; A= (x^2+3*C*cos(z)-2)/8*sqrt (abs (T^2-x^2));…
A: Result of c program
Q: Define a function S : Z+ → Z+ as follows. For each positive integer n, S(n) = the sum of the…
A: Here we have given function definition and solved s(n)
Q: Fibonacci numbers F1, F2, F3, . . . are defined by the rule: F1 = F2 = 1 and Fk = Fk−2 + Fk−1 for k…
A: In the question, it is given: Fk = Fk-2 + Fk-1 for k > 2 with F1=F2=1 ---(i) Lk = Lk-2 + Lk-1 for…
Q: Q1/ Simplify the following Boolean functions, using k-maps: a) F(A, B, C, D) = E (0, 1, 2, 4, 5, 7,…
A: (Disclaimer: Since you have asked multiple questions, we will solve the first 3 questions for you.…
Q: In RSA: a. Given n = 221 and e = 5, find d. b. Given n =3937 and e =17, find d. c. Given p = 19, q =…
A: Here, we are going to find out the values as per given question. In RSA, as we know that We have to…
Q: Given x=[1 1 0] and y=[1 0 2] find h[3] of h[n]=x*y O 2 O 1 O 3
A: Answer : Option D
Q: • The Domain of f(x) = V1- x is 1. [-1, 0) 2. (-0, 1] 3. (-0, 1) 4. [1, c0) 1 0 2 O 3 O 4 O
A: f(x)=(1-x)1/2=sqrt(1-x) Domain: Under root should not be negative quantity. So Domain : 1-x>=0…
Q: 1) Give the definition of the big U! What is the Big-O of the following functions: f(n) = 4n2 +3n…
A: As per our guidelines, we are supposed to answer only 1st three parts. Kindly repost the remaining…
Q: 1. Suppose that a and b are integers such that a = 45 (mod 71) and b = 53 (mod 71). Find an integer…
A: Answer: I have given answer in the handwritten format.
Q: Q9/The minimum sum- of- products for the following function isF(A,B,C,D,E)=Σm(0,1,15,16,17)…
A: Here is the solution:
Q: Given A={1,2,3,4,5,6},B={4,5,6,7,8,9}. Compute (e)B⊕A= (f) (A−B)∩(B−A) =
A: Given: Given A={1,2,3,4,5,6},B={4,5,6,7,8,9}. Compute (e)B⊕A= (f) (A−B)∩(B−A) =
Q: Find f(1), ƒ (2), ƒ (3), and f (4) if ƒ (n) is defined recur- sively by f(0) = 1 and for n = 0, 1,…
A: As per our guidelines, only one question or three sub parts will be answered. So, please repost the…
Q: Problem 4. Please show the followings: (a) let x and y be real numbers with 0 1 and b > 1.
A: Proved the given functions
Q: Q1. Given a sequence x(n) for Osn<3 , where x (0) =1, x (1) =2, x (2) =3 and x (3) =4, Evaluate its…
A: DFT stands for Discrete Fourier Transform, used for discrete and periodic signals. The discrete…
Q: Show that (a*b) O (b*c) Ð (c*a) = (a © b) * (b Ð c) * (c O a). Let (L,a ^ b = a ea v b=b.
A: Using boolean logic to solve.
Q: You are given a sequence of integers A1, A2,..., AN and an integer M. For any valid integers p, q,…
A: Here is the detailed python code for the given problem statement:
Q: Given the function T(n) = n3 + 20n + 5, show that T(n) is O(n3)
A: The Big-Oh definition says that, T(n) is O(n3 ) if T(n) ≤ c·n 3 for some n ≥ n0. This condition will…
Q: python WAP to find x+x^2+x^3+x^4+x^5 and take x from user
A: Requirements :- python WAP to find x+x^2+x^3+x^4+x^5 and take x from user Solution :- take user…
Q: (a) Show that 3x(Px x Px). (b) Show that {Qx,V y(Qy → Pz)} EX Px.
A: The solution for the above-given question is given below:
Q: d = F4(W, X, Y, Z) = Em(0, 2, 3, 5, 6, 8) K-map for d: wx\YZ 00 01 11 10 00 01 0. 1 11 X. 10 1 101
A: Note: we had provided solution according to given K-map Table
Q: 4. Consider f(n) = 3n2 + 4n – 3, mathematically show that f(n) is O(n?), 2(n²), and O(n2).
A:
Q: Suppose N is an RSA modulus, and x^2 ≡N y^2, but x≡N ±y. Show how to efficiently factor N when such…
A: RSA is the most far and wide and utilized public key calculation. Its security depends on the…
Q: Given a sequence x(n), n from 0 to 3, where x(0)=-2,x(1)=4, x(2)=0 and X(3)= Evalute its DFT X(K)
A: DFT OF THE GIVEN SEQUENCE X(K) 7 -2 + 1j -11 + 0j -2 - 1j
Q: n-17 .. n. For example, if n = 4 and k = 2, a solution is: [ [2,4], [3,4], [2,3], [1,2], [1,3],…
A: Machine independent language :- > the language which does not depend on the computer or its parts…
Q: Simplify the following Boolean expressions, using four-variable K-maps: x′z+w′xy′+w(x′y+xy′)
A: The given Boolean expression is: Fw,x,y,z=x'z+w'xy'+wx'y+xy' we can expand the last term, then the…
Q: Simplify the following Boolean function, using three-variable maps: F1(x, y, 2)=E (0, 2, 4, 5, 6)…
A: Answer : option " c " is correct answer F = z' + xy'
Q: (a) Show that (Vx)(A → B) – (3x)A → B, provided x does not appear free in B. (b) Suppose f is a…
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Q: 2. Convert the following regular expression to nondeterministic finite automaton. r = (0+ 1)*000(0+…
A: According to guidelines, we can only answer 1 question at a time, please repost the remaining…
Q: Q10/the minimum sum- of- products for the following function…
A: A'CDE+A'BC'D'E+A'B'C'+A'B'C+A'B'C. Explanation: Approach to solving the question: 1) First, we use…
Q: (x^3+2x)/(2x+1) is O(x^2).
A: According to Big oh definition The function f(x) is O(g(x)) for the values of the constants of c and…
Q: Construct a non- deterministic finite automaton (NFA) for below given regular expression: (0 U 1)*…
A: Non-deterministic Finite Automata(NFA): NFA is easy to construct when compared to DFA. It has more…
Q: Find A x B x C where A = {3,8}, B = {11, 18} , C = {0} . O None of these O (3,11,0), (3, 18,0),…
A: Option (c) is correct option.
Q: Given a digraph D = (V; A; `) in which all but one arc (u; v) have non-negative lengths, describe an…
A: The above algorithm is Bellman-Ford algorithm.
Q: Q. 5:1 show that: Let n and k be positive integers with n >= k. Use an algebraic proof to n+ 1 C(n +…
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Q: Let fand g be functions from the set of integers or the set of real numbers to the set ofreal…
A: Note: as per company guidelines we are supposed to answer only first 3 question at a time. please…
Q: Write a program computing terms of the sequence given by the condition: x_0=1, x_1=1/3,…
A: The question is to write the code for the given problem. As no language has been mentioned, C…
Q: 3. Consider a function: ( 1,ifn = 1 f(n) = 2. f(n – 1) + 1, ifn > 1 What is f(5) ?
A: The value of f(5) is calling f(4)+1, f(3)+1,f(2)+1,f(1)=
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- f : {1, 2, 3} ® {a, b, c, d} f(1) = c f(2) = b f(3) = a g : {a, b, c, d} ® {x, y, z} g(a) = y g(b) = x g(c) = x g(d) = z Find the composition gof4. Let N(x) be the statement “x has visited North Dakota,” where the domain consists of the students in your school. Express each of these quantifications in English. a) ∃x N(x) b) ∀x N(x) c) ˺∃x N(x) d) ∃x ˺N(x) e) ˺∀x N(x) f ) ∀x ˺N(x)Q1.nq. Given a 2d grid map of '1's (land) and '0's (water),count the number of islands.An island is surrounded by water and is formed byconnecting adjacent lands horizontally or vertically.You may assume all four edges of the grid are all surrounded by water. Example 1: 11110110101100000000Answer: 1 Example 2: 11000110000010000011Answer: 3""" def num_islands(grid): count = 0 for i in range(len(grid)): for j, col in enumerate(grid[i]): if col == 1: dfs(grid, i, j) count += 1 Please code it. .
- passing through (9,5) with x-int ecept -3A = [15, 12, 13, 19, 14, 10, 16, 20, 9, 18, 8, 7]B = [19, 14, 8, 16, 20, 9, 18, 15, 12, 13, 7, 10]vN = 0for i in range(len (A)):vN = A[i]for j in range(len (B)):if B[j] ==vN:print ('A[',i,'] with B[',j,']') implementation this code with JUST one for loopCount consecutive summers def count_consecutive_summers(n): Like a majestic wild horse waiting for the rugged hero to tame it, positive integers can be broken down as sums of consecutive positive integers in various ways. For example, the integer 42 often used as placeholder in this kind of discussions can be broken down into such a sum in four different ways: (a) 3 + 4 + 5 + 6 + 7 + 8 + 9, (b) 9 + 10 + 11 + 12, (c) 13 + 14 + 15 and (d) 42. As the last solution (d) shows, any positive integer can always be trivially expressed as a singleton sum that consists of that integer alone. Given a positive integer n, determine how many different ways it can be expressed as a sum of consecutive positive integers, and return that count. The number of ways that a positive integer n can be represented as a sum of consecutive integers is called its politeness, and can also be computed by tallying up the number of odd divisors of that number. However, note that the linked Wikipedia de0inition…
- Write Python Code Farmer John is worried for the health of his cows after an outbreak of the highly contagious bovine disease COWVID-19.In order to limit transmission of the disease, Farmer John's N cows ( 2<=N<=105) have decided to practice "social distancing" and spread themselves out across the farm. The farm is shaped like a 1D number line, with M mutually-disjoint intervals (1<=M<=105) in which there is grass for grazing. The cows want to locate themselves at distinct integer points, each covered in grass, so as to maximize the value of D, where D represents the distance between the closest pair of cows. Please help the cows determine the largest possible value of D. INPUT FORMAT (file socdist.in): The first line of input contains N and M. The next M lines each describe an interval in terms of two integers a and b, where 0<=a<=b<=1018. No two intervals overlap or touch at their endpoints. A cow standing on the endpoint of an interval counts as standing on…Count consecutive summers def count_consecutive_summers(n): Like a majestic wild horse waiting for someone to come and tame it, positive integers can be broken down as sums of consecutive positive integers in various ways. For example, the integer 42 often used as placeholder in this kind of discussions can be broken down into such a sum in four different ways: (a) 3 + 4 + 5 + 6 + 7 + 8 + 9, (b) 9 + 10 + 11 + 12, (c) 13 + 14 + 15 and (d) 42. As the last solution (d) shows, any positive integer can always be trivially expressed as a singleton sum that consists of that integer alone. Given a positive integer n, determine how many different ways it can be expressed as a sum of consecutive positive integers, and return that count. The count of how many different ways a positive integer n can be represented as a sum of consecutive integers is also called its politeness, and can be alternatively computed by counting how many odd divisors that number has. However, note that the linked…Given the following sets: U= {1,2,3,4,5,6,7,8,}, A={1,4,5,7}, B= {2,5,6,7,}, and C= {3,4,6,7} Complete the following set operations: a. A U(BUC) b. (A N (B N C))' . c. (A N B) U ( A N C) d. (A N B')U (A N C')
- 4.2) (L4) Give truth values for the propositional variables that cause the two expressions to have different truth values. For example, given p ∨ q and p ⊕ q, the correct answer would be p = q = T, because when p and q are both true, p ∨ q is true but p ⊕ q is false. Note that there may be more than one correct answer. r ∧ (p ∨ q) (r ∧ p) ∨ qComputer Science There is an n × n grid of squares. Each square is either special, or has a positive integer costassigned to it. No square on the border of the grid is special.A set of squares S is said to be good if it does not contain any special squares and, starting fromany special square, you cannot reach a square on the border of the grid by performing up, down,left and right moves without entering a cell belonging to S. 5 3 4 9 4 X 3 6 1 9 X 4 1 2 3 5 - Design an algorithm which receives an arbitrary n × n grid, runs in time poly-nomial in n and determines a good set of squares with minimum total cost.Not pseudocode Suppose the economies of the world use a set of currencies C1, . . . , Cn; think of these as dollars, pounds, Bitcoin, etc. Your bank allows you to trade each currency Ci for any other currency Cj, and finds some way to charge you for this service. Suppose that for each ordered pair of currencies (Ci, Cj ), the bank charges a flat fee of fij > 0 dollars to exchange Ci for Cj (regardless of the quantity of currency being exchanged). Describe an algorithm which, given a starting currency Cs, a target currency Ct, and a list of fees fij for all i, j ∈ {1, . . . , n}, computes the cheapest way (that is, incurring the least in fees) to exchange all of our currency in Cs into currency Ct. Also, justify the its runtime. [We are expecting a description of the algorithm, as well as a brief justification of its runtime.]