Suppose a = 3 (mod 12) and b = 8 (mod 12) where a and b are integers. Find the integer c with 0 < c < 11 such that c = 8a (mod 12). a) 0 b) 3 c) 5 d) 8

Q: 2.Suppose a | b and a | c, then it follows that there are integers s and t with b = as and c = at.…

A: 2. a | b it means that if b divides a then it give the reminder 0 and quotient value is integer. So…

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 :- &gt; the language which does not depend on the computer or its parts…

Q: Given f(x)=x2+6x and g(x)=1−x2, find f+g, f−g, fg, and fg.    Enclose numerators and denominators…

A: f(x)= x2 + 6x  g(x) = 1 - x2  We have to find :-                  1 ) f + g  or f(x) + g(x) 2) f - g…

Q: Write a program that does the following: f(x) = x² – 3x 1) define and g(x) = cos(2.x) f(x) lim 2)…

A: The problem is based on the basics of matlab.

Q: Find y[n]=x[n]*h[n] x[0] = 2, x[1] = 3, x[2] = 5, x[n] = 0 for all other integers (n). h[0] = 2 ,…

A: Introduction Given x is an array of values and x[0]=2, x[1]=3, x[2]=5, x[n]=0 , for all other…

Q: Find y[n]=x[n]*h[n] x[0] = 2, x[1] = 3, x[2] = 5, x[n] = 0 for all other integers (n). h[0] = 2 ,…

A: Introduction Given x is an array of values and x[0]=2, x[1]=3, x[2]=5, x[n]=0 , for all other…

Q: You are given a sequence of 16N positive integers a1, a2, . . . , a16N · You may shuffle this…

A: Below is the Code`

Q: Let A = {x €N : 3 < x < 13}, B = {x € N : x is even}, and C = {x €N :x is odd}. (a) Find An B. (b)…

A: - The question is to solve the given problem of union and intersection. - Given A = {x ∈ N : 3…

Q: Find y[n]=x[n]*h[n] x[0] = 2, x[1] = 3, x[2] = 5, x[n] = 0 for all other integers (n). h[0] = 2 ,…

A: Given x is an array of values and x[0]=2, x[1]=3, x[2]=5, x[n]=0 , for all other values of n   Given…

Q: Your task is to find the sum of f(X , Y , Z) over all triplets (X, Y , Z) where X, Y and Z belong to…

A: GIVEN  Given a triplet of integers (X , Y , Z), such that X ≤ Y and Y ≥ Z, we define f(X , Y , Z) to…

Q: For example, given [10, 15, 3, 7] and k of 17 , return true since 10 + 7 is 17.

A: I have given the c++ code below.

Q: Let M = ({90, q1, 92}. {0. 1}, {0, 1, b}, 8, qo. {q2}) %3D where ô is given by d(g0. 0) = (q1, 1, R)…

A: Requirements :-       Approach:- Let w be the input string, By (R1) and (R2), M reads the entire…

Q: F'ind / (1), S(2), S (3), and f (4) if s(n) is defined recur- sively by f(0) =1 and for n 0, 1, 2,…

A: As per Bartleby guidelines “Since you have asked multiple question, we will solve the first question…

Q: Given two integer N and K, the task is to find sum of modulo K of first N natural numbers i.e. 1%K +…

A: Step 1:- Program Approach:- 1.Create the class SumOfModulo 2.This class contaion 3 data members n,k…

Q: if it's like m/(m+1) where m is any +ve integer. Suppo the number of pairs of integers i, j such…

A: According to the given problem statement we are required to develop a code  which print an output…

Q: 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…

A:

Q: For P= 0 and compute the value of K under the condition. if (P 1 && P 8)        K= P - 1 else…

A: For P = 0 ,  Operations :  if (P &lt;= 1)        K = P + 5else if (P &gt; 1 &amp;&amp; P &lt;= 5)…

Q: Consider a series of numbers given below. Identify the suitable Start, End and Interval values for…

A: option B

Q: The prime factorization of a given positive number N is the set of prime numbers that when…

A: #include &lt;stdio.h&gt;#include &lt;math.h&gt;void primeFactors(int n,int a[],int *num_factorsp){…

Q: L = {0n w |n 2 1, w E {0, 1}*, and w contains at least n 1's} and M = {0n w |n 2 1, w E {0, 1}* ,…

A: a) for n &gt;=1, Regular expression for 0^n =&gt; 0* at least n 1's means &lt;= n therefore regular…

Q: If P(x) is a polynomial in x with integer coefficients, let W(P(x)) = number of odd %3D coefficients…

A: Procedure: We have the 2 input Input1 and Input2 from the user use these input defines on the…

Q: Given five positive integers, find the minimum and maximum values that can be calculated by summing…

A: PROGRAM CODE: #include &lt;bits/stdc++.h&gt;       // include header file for standard c++ library…

Q: Let M = ({q0, 91, 92}. {0, 1}, {0, 1, b}, 8, qo. {q2}) where & is given by d(q0. 0) = (41, 1, R)…

A: Let's understand step by step :   Turing machine is having 7 tuples : T(M) = {Q , Σ , T , B , δ , q0…

Q: Find the smallest value of n such that f(x) is O(x^n) for each of the following. a) 3x^2-4x +12 b)…

A: 3x^2-4x +12 = 3x^2-4x = x^2-x = x^2 O(x^n) = x^2 n = 2 or 2 degree polynomial

Q: You are given a sequence of integers A1, A2, ..., AN and an integer M. For any valid integers p, q,…

A: As per the specification given in the question , this will be the required python Read the commented…

Q: Ex: Let A1 ={x, y}, A2 ={1, 2}, and A3 ={a, b}, (A1 x A2) x A3, A1 × A2 × A3. Find A1 x A2,

A: Given: Ex: Let A1 ={x, y}, A2 ={1, 2}, and A3 ={a, b}, Find A1 × A2=? (A1 × A2) × A3=? A1 × A2 ×…

Q: Let f(n) = 2n and g(n) = n. a) Show that f is O(g) using specific values of C and no. b) Show that g…

A: Big-O Notation O(n): Let f(n) and g(n) be the two functions described and the function f is said to…

Q: all integers between -4 and 4, and the domain for y consists of all real numbers. Determine the…

A: As per the answering guidelines, solving first 3 sub question 1. There exists some x and for all y…

Q: If A=[1,2,3;4,5,6;7,8,9], then B=A([1 2],[1 2]) is

A: Given A = [1,2,3; 4,5,6; 7,8,9] So, A looks like 123456789

Q: The Virtual Weight (vW) of an integer number (which consists of more than 1 digit) is the sum of the…

A: The program prompts the user to enter a number between 5 and 20. The user is prompted to do so until…

Q: The Virtual Weight (VW) of an integer number (which consists of more than 1 digit) is the sum of the…

A: A C++ program is as follows, File name: “main.cpp” #include&lt;iostream&gt; #include &lt;cstdlib&gt;…

Q: Let A = {m ∈ Z | m ≡ 9 (mod 12)}. Let B = {n ∈ Z | n ≡ 1 (mod 4)}.

A: We are going to prove that set B is not a subset or equal to set A. First find out what is set A and…

Q: Trace the following program MOV BX, 708EH MOV AX, BX MOV CX, 4802H OR BL, BH XOR BL, AH SHL BL, 01H…

A: Assembly language is a low-level programming language for a computer or other programmable device…

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: Put 0, 0, N in the right position, the same as the given example a) n² = .- (n), solution: n2 =…

A: First of all, we need to define the symbols as follows. θ = equal function(average case) O = worst…

Q: L= {xϵ∑= {0,1} |x=0n1n for n>=1};

A: Answer: The correct answer to the given question is option (ii) "No".

Q: FP(x, n) if n==1 return x return FP(x*x, n/2) return x*FP(x*x, (n-1)/2) if n is even else Given a…

A:

Q: Consider the function, f(n), defined by the following code int f(int n) {     int r = 0;     if (…

A: This question is related to time complexity in algorithm and we have to calculate the time…

Q: Let f(n) = 2n – n² + 10n – 7. Show that f(n) is O(n³) using specific values of C and no-

A: Let f(n) = 2n3 − n2 + 10n − 7. Prove that f(n) is O(n3). using specific values of C and n0.

Q: ction that given integers j and k where j ≥ 2 that then j is not divisible by k or(∨) j is n

A: Proof by contradiction is a type of verification that builds up reality or the legitimacy of a…

Q: Problem 5. Prove that n³ e O(1.2"), but n³ ¢ O(1.2"). You may use the facts that log(n) E O(n) but n…

A: Proved the given asymptotic function

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: If f = (log n)^2, g = n log n; what is the relationship between f and g? Choose all that applies.…

A: In this question, we are given two functions  f= (log n)^2, g = n log n and we to tell the…

Q: Suppose team A plays in a best-of-7-game series. In sports sometimes teams play in a series until…

A:

Q: Suppose that f(x) is O(g(x)).   Does it follow that 2f(x) is O(2g(x))?   Prove your answer.

A: The given information is: f(x) is O(g(x)).

Q: Homework 2 1. y = 3x* - 5x + 6x – 7 find z dy 2. Ify' - 3xy + x = 5, find d dr 'dr ' dx dx

A: dh/dx

Q: Let A = {1, 3, 5, 7, 9}, B = {0, 2, 4, 6} and C = {1, 2, 3, 4, 5, 10}. What is the result of…

A: We need to find the correct answer for the expression (A U B) ∩ C We have values of A, B, C are-  A…

Q: What is the value of X after solving the following equation? X = ((5^ 2/ 5) ^2 + 5) - 10 * 4/2 + 12…

A: It will solve according to priority operator ^  mod / and *  left to right + and - left to right

Q: Let U {0, 1, 2, ...,9}, A = {0, 3, 5, 8}, B = {0,1,2, 3, 6}, and C = {2,3,5, 8, 9}. AUBUC= AU (Bn C)…

A: We are given A universal set U, and other 3 sets A, B and C. We are going to perform given…

Q: 2) Trace the following program MOV BX, 708ЕН MOV AX, BX MOV CX, 4802н OR BL, BH XOR BL, AH SHL BL,…

A: Here we need to trace the above assembly language program or we can say that we need to write all…