Let MAJ : {0, 1}³ {0,1} and NOT : {0,1} → {0, 1} be defined as in lecture. Let 1: {0, 1}° {0, 1} simply give the constant value 1 Prove that {MAJ, NOT, 1} is equivalent to AND, OR, NOT. In other words, show that any function that can be computed by AND,OR,NOT can also be computed using combinations of {MAJ, NOT, 1}, and vice-versa.

Let MAJ : {0, 1}³ {0,1} and NOT : {0,1} → {0, 1} be defined as in lecture. Let 1: {0, 1}° {0, 1} simply give the constant value 1 Prove that {MAJ, NOT, 1} is equivalent to AND, OR, NOT. In other words, show that any function that can be computed by AND,OR,NOT can also be computed using combinations of {MAJ, NOT, 1}, and vice-versa.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

See similar textbooks

Similar questions

Find (f o g) and (g o f) , where f (x) =x2+1 and g(x) = x + 2, are functions from R to R.
Let X= (-3,-2,-1,0, 1}. Let f: X→ N by f(x) = [7z+11: The range of the function is
2. For the given Boolean function: F (A,B,C,D,E) = X(0, 2,3,4,5,6,7,11,15,16,18,19, 23,27,31) Show the area enclosed and label it with the corresponding literal, legibly. Obtain the simplest function in sum of product form and product of sum form using map method
Generate a real life world problem about quotient of functions on operation. Then solve it.
Simplify the given function using K map f(a,b,c,d)= ∑m (1, 2, 4, 11, 13, 14, 15) + d (0, 5, 7, 8, 10)
Consider the function f(x) = arctan(2(x − 1)) – In |x|. Plot (using PYTHON ) the graph of the function f(x) and describe the intervals of monotonicity of the function f. Speak also about the roots of the equation f(x) = 0. (a) (b) Prove by analytical means (using Calculus), that the equation f(x) = 0 has exactly four real roots P1 < P2 < P3 < P4.
For the function f: Z Z prove or disprove whether f is injective and/or surjective f(x) = 4x –6 %3D
Let f: A→B and g: B→C be two functions. If g◦f is a one-to-one function, prove that f is one-to-one
We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b] . Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1, X2, ..., Xn,..., XN. Each interval is Ax = (b – a)/N. The Simpon numerical integration rule is derived as: N-2 Li f(x)dx = * f(x0) + 4 (2n odd f(xn)) + 2 ( En=2,n even N-1 f(x,) + f(xn)] . Now complete the Python function InterageSimpson(N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is f (x) = 2x³ (Already defined, don't change it). In [ ]: # Complete the function given the variables N,a,b and return the value as "TotalArea". # Don't change the predefined content, only fill your code in the region "YOUR CODE" from math import * def InterageSimpson (N, a, b): # n is…
We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b] . Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1, x2,.. Xn,..., XN. Each interval is Ax = (b − a)/N. The equation for the Simpson numerical integration rule is derived as: f f(x) dx N-1 Ax [ƒ(x0) + 4 (Σ1,n odd f(xn)) ƒ(x₂)) + f(xx)]. N-2 + 2 (n=2,n even Now complete the Python function InterageSimpson (N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is ƒ(x) = 2x³ (Already defined in the function, no need to change).
Explain the Wronskian determinant test. Using the Wronskian determinant test, write the program using NumPy to determine whether the functions f(x)=e^(- 3x), g(x)=cos2x and h(x)=sin2x are linearly independent in the range (-∞, + ∞). #UsePython
We have learned the mid-point and trapezoidal rule for numercial intergration in the tutorials. Now you are asked to implement the Simpson rule, where we approximate the integration of a non-linear curve using piecewise quadratic functions. Assume f(x) is continuous over [a, b]. Let [a, b] be divided into N subintervals, each of length Ax, with endpoints at P = x0, x1,x2,..., X., XN. Each interval is Ax = (b − a)/N. The equation for the Simpson numerical integration rule is derived as: f f(x)dx ≈ [ƒ(x0) + 4 (EN-1,n odd S(x)) + 2 (Σ2²n even f(x)) + f(XN)]. Now complete the Python function InterageSimpson (N, a, b) below to implement this Simpson rule using the above equation. The function to be intergrate is f(x) = 2x³ (Already defined in the function, no need to change). *Complete the function given the variables N, a,b and return the value as "TotalArea"." "Don't change the predefined content' only fill your code in the region *YOUR CODE"" from math import * def InterageSimpson (N, a,…