Let multidimensional array a with size 3x4 be {1,2,3,4,5,6,7,8,9,10,11,12} and b be the last digit of your student number. Accordingly, if we run the given functions in the following order, what will be the output? Explain step by step. b= 5 function1(b); print(A,b); function2(A,b); print(A,b); function3(A[b%4][b%3],b); print(A,b);
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- In this question, we are going to write a Racket functionwordMaxIndex that calculates the maximum index of each word thatappears in an input word list. For example, if the input is’(time is long but life is short)Then one output can be((time 0) (long 2) (but 3) (life 4) (is 5) (short 6))The index of the first word in a word list is 0; the index for the secondword is 1; etc. Therefore, in the previous example, the maximum indexfor word “time” is 0; the maximum index for word “is” is 5, since “is”appears twice, at index 1 and 5. Note that you are not asked to sortthe words in the output. Therefore, the output is correct as long asthe indexes are correct.Do the following steps to implement the word-index program. In ourdiscussion, we call a word with an index a word-index pair, for example,(short 6) and (is 5) are word-index pairs. We call a list of word-index pairs a word-index list.(a) Write a function initialWIList that takes a list ofwords and creates a word-index list. The resulting…Computer Science Prove that the set M = {x ∈ R: x 2 = 2a3 b , a ∈ N, b ∈ N} is countably infinite. Your solution should either give a bijective function f : N → M or give pseudo-code of a program that prints all the values of such a function, in the following format (in this case you don’t have to define f explicitly, but need to also show the first five lines of output): 0: element of M 1: another element of M 2: yet another element of MWrite a function solver that takes a non-negative integer upper_bound as an argument, and prints all non-negative integers i line-by-line in ascending order such that i is at most upper_bound, and i+100 and i+268 are perfect squares. Note that the function solver prints the numbers instead of returning them, but you may want to define a helper function is_perfect_square to return whether a number is a perfect square.
- SUCCESSIVE-OVER-RELAXATION Method TROUBLESHOOTING: Fix the errors in the code below and run the script with your modified code function [x,numIter,omega] = gaussSeidel(func,x,maxIter,epsilon) % Solves Ax = b by Gauss-Seidel method with relaxation. % USAGE: [x,numIter,omega] = gaussSeidel(func,x,maxIter,epsilon) % INPUT: % func = handle of function that returns improved x using % x = starting solution vector % maxIter = allowable number of iterations (default is 500) % epsilon = error tolerance (default is 1.0e-9) % OUTPUT: % x = solution vector % numIter = number of iterations carried out % omega = computed relaxation factor if nargin < 4; epsilon = 1.0e-9; end if nargin < 3; maxIter = 500; end k = 10; p = 1; omega = 1; for numIter = 1:maxIter xOld = x; x = feval(func,x,omega); dx = sqrt(dot(x - xOld,x - xOld)); if dx < epsilon; return; end if numIter == k; dx1 = dx; end if numIter == k + p omega = 2/(1 + sqrt(1 - (dx/dx1)ˆ(1/p))); end end error(’Too many iterations’)5. Let R = {1, 3, π, 4, 1, 9, 10}, S = {{1}, 3, 9, 10}, T = {1, 3, π}, and U = {{1, 3, π}, 1}. Which of thefollowing are true? For those that are not, why not? (d) 1 ⊆ U(e) {1} ⊆ T(f) {1} ⊆ S(g) {1} ∈ SA triple (x, y, z) of positive integers is pythagorean if x2 + y2 = z2. Using the functions studied in class, define a function pyth which returns the list of all pythagorean triples whose components are at most a given limit. For example, function call pyth(10) should return [(3, 4, 5), (4, 3, 5), (6, 8, 10), (8, 6, 10)]. [Hint: One way to do this is to construct a list of all triples (use unfold to create a list of integers, and then a for-comprehension to create a list of all triples), and then select the pythagorean ones. def unfold[A, S](z: S)(f: S => Option[(A, S)]): LazyList[A] = f(z) match { case Some((h, s)) => h #:: unfold(s)(f) case None => LazyList() } code in scala
- For each of the following functions, indicate the class (g(n)) the function belongs to. (Use the simplest g(n) possible in your answers.) Please show work to prove the assertions.Consider the function, f(n), defined by the following code int f(int n) { int r = 0; if ( n % 2 == 0 ) return 1; // when n is even while ( n > 1 ) { n = n – 3; r++; } return r; } From the definitions of big-Theta and little-oh: Prove or disprove that f(n) is Θ ( n ) 2. Prove or disprove that f(n) is o ( n^2 ) ( note: function f(n) as defined by the code, that is, the return value, and is not asking about the runtime of the code.)Prove or disprove:(a)∃ sets A,B ∀ functions f: A→B, f is a bijection. (b) if f : A → B is a function, C ⊆ A, and D ⊆ B, then f : C → D is always a function.[Note 1: one is true, the other is false.][Note 2: feel free to draw bubble-arrow pictures here, but make sure you explain what’s going on very carefully.]
- We have been working extensively with the predicate "eventually greater than" defined on pairs of functions f of g. Which of the following is equivalent to f(x) is not eventually greater than g(x)? (Select all that apply) Group of answer choices ¬((∃x0)(∀x)(x>x0→f(x)>g(x))) ((∃x0)(∀x)(x>x0→f(x)≤g(x))) (∀x)(∃x0)(x0>x→f(x0)≤g(x0)) (∀x)(∃x0)(x0>x→f(x0)≤g(x0))Write a function linear_independence that takes a collection of vectors with integer entries (each written as a list), and returns True if this collection of vectors is linearly independent, and False otherwise. Examples: linear_independence([1,2]) should return True. linear_independence([1,3,7],[2,8,3],[7,8,1]) should returnTrue. linear_independence([1,3,7],[2,8,3],[7,8,1],[1,2,3]) should return False.For this question, you will be required to use the binary search to find the root of some function ?(?)f(x) on the domain ?∈[?,?]x∈[a,b] by continuously bisecting the domain. In our case, the root of the function can be defined as the x-values where the function will return 0, i.e. ?(?)=0f(x)=0 For example, for the function: ?(?)=???2(?)?2−2f(x)=sin2(x)x2−2 on the domain [0,2][0,2], the root can be found at ?≈1.43x≈1.43. Constraints Stopping criteria: ||?(????)||<0.0001|f(root)|<0.0001 or you reach a maximum of 1000 iterations. Round your answer to two decimal places. Function specifications Argument(s): f (function) →→ mathematical expression in the form of a lambda function. domain (tuple) →→ the domain of the function given a set of two integers. MAX (int) →→ the maximum number of iterations that will be performed by the function. Return: root (float) →→ return the root (rounded to two decimals) of the given function.