Let E1 = {a}, E2 = {a, b} and N be the set of natural numbers. Using a bijective function, a. prove that | E,*| = |N|.
Q: Simplify the following function using k-maps. F(X,Y)=X+X'Y
A: We have to simplify the given boolean function using k-map. In k-map number of cells depends on…
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: The polynomial function f is defined by f(x)=2x² + 3x³ +5x²-x-5. Use the ALEKS graphing calculator…
A:
Q: Use a software program or a graphing utility to solve the system of linear equations. (If there is…
A: I am using a software program (SCILAB/MATLAB) to get output of x1,x2,x3,x4,x5; Matrix fwe can form…
Q: More asymptotic notation. Let f, g, h : N → R2º. Prove or disprove that if f +gE O(h), then f E O(h)…
A: The solution for the above given question is given below:
Q: Give an explicit formula for a function from the set of all integers to the set of positive integers…
A: given: explicit formula for a function from the set of all integers tothe set of positive integers…
Q: Prove or disprove that, for any regular expressions R and S, (R*S*)* = (R + S)*
A: Answer: Proof: (R+S)* = (R*+S)* = R*(R+S)* = (R+SR*)* = (R*S*)* ( OR) -> R,S belongs to R*S*…
Q: Show that if a, b, c, and mare integers such that m≥2, c > 0, and a≡b (mod m), then ac ≡bc (mod mc).
A: According to the question, we have to prove that ac ≡ bc (mod mc). And we have given that a, b, c,…
Q: You are explaining the problem of searching for a move in chess to your friend. Your friend notices…
A: The strategy wouldn't work since the differentiation is not guaranteed to give a maxima always,…
Q: Determine whether the function f(x) = 4x−1 where f:R→R is a bijection. If it is not, explain why…
A:
Q: For £ = (a,b}, give a regular expression r such that L(r) = (wE £*: whas at least one pair of…
A: Defined the regular expression for the given language
Q: Given f1(x) = −3x + 4 and f2(x) = x2 are functions from R to R. Find: a. f1.f2(x) b. f1.f2(-1)
A: Answer: The solutions of both the parts are given below-
Q: log 2 (x +3) x2 +3x + 2 Find the domain of definition of f (x)=
A: Solution :-_
Q: Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + *1 and g(x) =…
A: Answer: fog(x) = 6x+9
Q: Use the Pumping Lemma with length to prove that the following language is non-regular: L = {a²bn an,…
A: We need to prove that L is non-regular, using Pumping lemma.
Q: 5. Simplify the following functions using a K-map: h)F(W,X,Y,Z)=X'Y'Z'+XYZ'+WXY+W'X'Y'+WZ
A:
Q: Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) =…
A: If there are two functions f and g such that f : X ->Y g: Y -> Z then the function…
Q: justify whether each of the following functions is injective, surjective, bijective, or none of…
A: following function is surjective
Q: 5. Simplify the following functions using a K-map: e)F(X,Y,Z)=X'Y'Z'+X'YZ+XY'Z+XYZ
A: F(X,Y,Z) = X'Y'Z' + X'YZ + XY'Z + XYZ where, No. of variables is 3 i.e. x, y, z
Q: Find the points of inflection of the graph of the function. (Round your answers to three decimal…
A: The inflection points of f(x)=7sin(x)+sin(2x) on the interval [0,2π]: (x,y) = ( π-atan (157),-sin (…
Q: Use the Pumping Lemma with length to prove that the following language is non-regular: L = {a²ba",…
A:
Q: (c) Let L be the language of all equations anX" + a1Xd-1+...+ ad-1X +ad = 0, with unknown X and…
A: Answer: I have given answered in the handwritten format in brief explanation.
Q: Exercise 1: Z1 ', and express it in a + bi Z2 Given that Z1 = 1 – 2i, z2 =-3+4i. Find form.
A: Given details are:- z1 = 1-2i z2 = -3+4i To find:- z1 / z2
Q: By using the Big-O definition and formal proof, show and prove that a function y=n*+3 can't belong…
A: For a given function g(n), we have set O(g(n)) = { f(n) : there exist positive constants c and n0…
Q: 5. Show that for every partially computable function f(x,,..., x,), there is a number m 2 0 such…
A: Answer: I have given answered in the handwritten format
Q: . Let Q, R and S be sets. Show that (R – Q) ∪ (S – Q) = (R ∪ S) – Q.
A: Given: Let Q, R and S be sets. Show that (R – Q) ∪ (S – Q) = (R ∪ S) – Q.
Q: Determine whether or not the function f : Z × Z ! Z is onto, if f((m, n)) =m-n.
A: Determine whether or not the function f : Z × Z ! Z is onto, if f((m, n)) =m-n.
Q: Q1/ Simplify the following Boolean functions in products of sums using K-map: (0, 2, 5, 6, 7, 8, 10)…
A: Given Query: 1. F(w,x,y,z) = Minterms(0,2,5,6,7,8,10) 2. F(A,B,C,D) = Maxterms(1,3,5,7,13,15)
Q: Use the Pumping Lemma with length to prove that the following language is non-regular: L = {a²b" a",…
A: Given language is, L={a2bnan, n>0} Pumping Lemma of regular language states that, if the infinite…
Q: Define a function S:z* → z* as follows. For each positive integer n, S(n) =the sum of the positive…
A: Since the programming language is not mentioned so I have used the C++ programming language.…
Q: Let S and T be sets with: |S| = 5, |T| = 7 %3D How many one-to-one functions are there from S to T?…
A: There are D. 7!/2 one-to-one functions from S to T.
Q: Let f : Z → Z be some function over the integers. Select an appro- priate proof technique (direct,…
A: Answer: I have given answered in the handwritten format in brief explanation
Q: Let set S = {n/n eZ and n is negative), and f be a function defined as f: N S (a) Prove that…
A: The solution to the given question is:
Q: Wilson's Theorem states that for any natural number n > 1, n is prime if and only if (n – 1)! = -1…
A: Introduction: Wilsons theorem states that a positive integer n>1 is a prime if and only if…
Q: (a) Show that (Vx)(A → B) – (3x)A → B, provided x does not appear free in B. (b) Suppose f is a…
A:
Q: Let Q(x, y) denote xy< 0 The domain of x is {1,2,3} and the domain of y is (0, -1, -2, -3).
A: Code: x = [1,2,3]y = [0,-1,-2,-3]for i in x: for j in y: if i*j<0:…
Q: and y be integers such that a = 3 (mod 10) and y = 5 (mod 10). Find the integer z such that 97x+3y³…
A:
Q: 3. If a and b are any two positive naturals, then the set {a + bi: i is a natural} contains…
A: Set a+bi cannot have infinitely many prime numbers.
Q: A Pythagorean triplet is a set of three natural numbers, a b c, for which, a^2 + b^2 = c^2 For…
A: Before we procced further let us do some fundamental maths! let a = m2 - n2 b = 2*m*n c = m2 +…
Q: 2- Let be f(t) a real, periodic function satisfy f(-t)= -f(t), The general form of the Fourier…
A: A Fourier series is an extension of a periodic function f(x) in terms of an infinite sum of sines…
Q: Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) =…
A: EXPLANATION: Composition of function is basically the application of one kind of function to the…
Q: Can you represent the following Boolean function f(A, B) with a linear classifier? If yes, shov the…
A: Given Data : A B f(A,B) 0 0 1 1 1 1 0 1 0 1 0 0
Q: Write a program that returns the minimum of a single-variable function g(x) in a given region [a,…
A: It is defined as a powerful general-purpose programming language. It is used in web development,…
Q: efined, show that f ◦
A: It is defined as,
Q: Prove that if a is an integer that is not divisible by 3, then (a + 1)(a + 2) .is divisible by 3
A: Step 01: all integers a∈b is expressed as : a = 3q + r ; where r=0,1,2 If a is an integer that is…
Q: Give an explicit formula for a function from the set of integers to the set of positive integers…
A: A function f from A to B has the property that each element of A has been assigned to exactly one…
Q: Let fand g be functions from the set of integers or thes We say that f ( x ) is 0 ( g (x )), read as…
A: First is already solved , We will solve only 2,3,4 question. To get Remaining solved please repost…
(DiscreteMath)
Step by step
Solved in 3 steps with 3 images
- Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) = x ^2. The composition of fog (-2) is --Show that if f(x) and g(x) are functions from the set of real numbers to the set of real numbers, then f(x) is O(g(x)) if and only if g(x) is Ω(f(x)).Let f and g be functions from the set of integers or the set of real numbers to the set of real numbers. We say that f ( x ) is O ( g ( x ) ), read as "f ( x ) is big-oh of g ( x )", if there are constants C and k such that | f ( x ) | ≤ C | g ( x ) | whenever x > k. KINDLY SHOW YOUR SOLUTION. 7. Generating sequences of random-like numbers in a specific range. Xi+1 = aXi + c Mod m where, X, is the sequence of pseudo-random numbers m, ( > 0) the modulus a, (0, m) the multiplier c, (0, m) the increment X0, [0, m) – Initial value of sequence known as seed m, a, c, and X0 should be chosen appropriately to get a period almost equal to m For a = 1, it will be the additive congruence method. For c = 0, it will be the multiplicative congruence method
- Give an explicit formula for a function from the set of all integers tothe set of positive integers that is onto but is not one-to-one.How do we define that a function f(n) has an upper bound g(n), i.e., f(n) ∈ O(g(n))?justify whether each of the following functions is injective, surjective, bijective, or none of these categories: (N is the set of natural numbers, and Σ∗ is the set of all strings over Σ.) (a) h : Σ∗ → Σ∗, where Σ = {a, b}, and h(w) = wR
- If p, q are positive integers, fis a function defined for positive numbers and attains only positive values such that f(xf(y)) = x ^ p * y ^ q then prove that p ^ 2 = qLet f (f(n) and g(n)) be asymptotically nonnegative functions. Using the basic definition of Θ notation, prove that max(f(n), g(n)) = Θ(f(n) + g(n)),Suppose we have positive integers a, b, and c, such that that a and b are not relatively prime, but c is relatively prime to both a and b . Let n = s × a + t × b be some linear combination of a and b, where s and t are integers. Prove that n cannot be a divisor of c. Follow the definition of relative primes, and use contradiction.
- justify whether each of the following functions is injective, surjective, bijective, or none ofthese categories: (N is the set of natural numbers, and Σ∗ is the set of all strings over Σ.) (a) f : N → N , f(n) = n div 3(b) g : N → N , g(n) = n2 + 2n + 1 (c) h : Σ∗ → Σ∗, where Σ = {a, b}, and h(w) = a|w| (d) h : Σ∗ → Σ∗, where Σ = {a, b}, and h(w) = wRis this functions from R to R is a bijection or not f(x)=(x2+2)/(x2+3)Let Σ = {a, b}. Indicate whether or not L is regular and prove your answer. (i) L={w ∈ {a, b}* : w contains at least two a’s and at most three b’s}. (ii) L={a^ib^j : i, j ≥ 0 and i < j.}.