Problem 1. Prove that the following functions are Primitive Recursive. I – 1 if x > 0, (1) mPred(x) = for r € N. if x = 0. [1 if x > 0, 0if x = 0. (2) sgn(x) = for x E N. %3D if x > 0, (3) sgn(x) = for x Ν. 1 if x = 0.

Q: 5. Find the least integer n such that f(x) is 0(x") for each of these functions 5.a f(x) = 2x² + x³…

A:

Q: Recurrence relations: Master theorem for decreasing functions T(n) = {TG T(n −b) + f(n), if n = 0 if…

A: We need to find the recurrence relation using master theorem. I have given explanation in…

Q: 6 For the following pairs of functions, first decide whether f (n) dominates g(n), or g(n) dominates…

A: See the solution below-

Q: 4. Find a closed form representation for the function defined recursively by f(0) = 5 and…

A: Answer: We have explain in more details to correct using an inductive arguments

Q: for linear algebra in solving a sytem of linear equations in form AX = B. True or false. 1.the…

A: Here in this question we have given a linear equations inform of AX= B.and we have asked to comment…

Q: The Fibonacci function f is usually defined as follows. f (0) = 0; ƒ(1) = 1; for every n e N>1, f(n)…

A: Solution:   Given,     f(0) = 0 f(1)  = 1

Q: For (∃ x)(P(x,b)) Would an example of this being true if the domain was all the Avengers and x was…

A: Introduction: In logic and mathematics, quantifiers are used to express the existence or…

Q: 3. Use a truth table (either by hand or with a computer program) to prove the commutative laws for ^…

A: The commutative law for ∧ is p∧q≡q∧p lets create truth table for the law p q p∧q q∧p T T T T…

Q: Recurrence relations: Master theorem for decreasing functions T(n) (1, (aT(n-b) + f(n), = {aT(n- if…

A: According to the information given:- We have to find the T(n) of mentioned Recurrence relations:…

Q: (DL1) α V (βΛ γ)-(α V β) Λ(α V γ)

A: Below is the proof for DL1: