Answered: Let A = {1, 2, 3, 4, 5} and B = {2, 3,…

Let A = {1, 2, 3, 4, 5} and B = {2, 3, 4, 5, 6, 7} and C = {a, b, c, d, e} 17. Give an example of f: A -> B, g: B -> C such that (g o f) is 1-1 but g is not 1-1.

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

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Consider eight points on the Cartesian two-dimensional x-y plane. a g C For each pair of vertices u and v, the weight of edge uv is the Euclidean (Pythagorean) distance between those two points. For example, dist(a, h) : V4? + 1? = /17 and dist(a, b) = v2? + 0² = 2. Because many pairs of points have identical distances (e.g. dist(h, c) V5), the above diagram has more than one minimum-weight spanning tree. dist(h, b) = dist(h, f) Determine the total number of minimum-weight spanning trees that exist in the above diagram. Clearly justify your answer.
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x = 1; y = 2; z = 1; n = 5; while (z
Question 4 Please answer them correctly
1. Let i, i = 1,2,..., n + 1 different nodes and let yi € R, i = 1,2,...,n + 1. The interpolating polynomial is written in Newton's form as: Pn (x)= = a₁ + a₂(x − x₁) + a3(x − x₁)(x − x₂)+...+an+1(x − x₁)(x − Xn+1), where the coefficients ai, i = 1, ,...,n+ 1 can be computed using the following algorithm: Algorithm 1 Newton's polynomial aiyi, i = 1, 2, … … . n+1 for k= 2: n + 1 do for i 1 k-1 do ak = end for end for (akai)/(xk - Xi) If the coefficients a,, i = 1,..., n +1 are known, then the value of the interpolating polynomial at the point z can be computed using Horner's formula: Algorithm 2 Horner's formula S = an+1 for in-1:1 do s = a₁ + (2x₁) s end for Pn (2) = = S Remark: It is noted that in the loop conditions i=a:b:c of the previous pseudo-codes a is the starting value, the step and c the last value. (a) Write PYTHON 's functions coefs and evalp implementing the previously described algorithms for the coefficients of the interpolating polynomial and it's evaluation at values z…
Type in Latex **Problem**. Let $$A = \begin{bmatrix} .5 & .2 & .3 \\ .3 & .8 & .3 \\ .2 & 0 & .4 \end{bmatrix}.$$ This matrix is an example of a **stochastic matrix**: its column sums are all equal to 1. The vectors $$\mathbf{v}_1 = \begin{bmatrix} .3 \\ .6 \\ .1 \end{bmatrix}, \mathbf{v}_2 = \begin{bmatrix} 1 \\ -3 \\ 2 \end{bmatrix}, \mathbf{v}_3 = \begin{bmatrix} -1 \\ 0 \\ 1\end{bmatrix}$$ are all eigenvectors of $A$. * Compute $\left[\begin{array}{rrr} 1 & 1 & 1 \end{array}\right]\cdot\mathbf{x}_0$ and deduce that $c_1 = 1$.* Finally, let $\mathbf{x}_k = A^k \mathbf{x}_0$. Show that $\mathbf{x}_k \longrightarrow \mathbf{v}_1$ as $k$ goes to infinity. (The vector $\mathbf{v}_1$ is called a **steady-state vector** for $A.$) **Solution**. To prove that $c_1 = 1$, we first left-multiply both sides of the above equation by $[1 \, 1\, 1]$ and then simplify both sides:$$\begin{aligned}[1 \, 1\, 1]\mathbf{x}_0 &= [1 \, 1\, 1](c_1\mathbf{v}_1 +…
6. Let U={1,2,3,4,5,6,7,8,9,10} , A={ 2,3,4,7} B={ 1,4,8,9} , c={8,2,4}.Find the elements of each sets. (6 pts@3 pts each) a. (ANB)- (C- B) b. ( (CNA)-(B -A) )N c
Write the PYTHON programming to solve with breadth-first search and build node-arcs with python code for the attached problem:
Create an R function pwfun(), which computes values of the piece-wise (mathematical) function pwfun defined in the following way: x < -1 Its graph is as follows. e pwfun(c(-2, 0.5, 3)) 208 pwfun(x) = - x = c(-3, -2, -1, 0, 1, 2, 3.2) pwfun(x) 4 2 0 0 0 39.24 -2x-2 0 x²-1 18 Your R function pwfun() should also accept x as a vector of arbitrary length and return vector of the same length with entries defined as values of the mathematical function pwfun, evaluated at the corresponding entries of vector x. Here are some input vectors and what you should get as a corresponding output. pufun(-1) .-1≤x≤1 1
4. Let E = {a, b}. Prove the equivalence: b+ e*bab((ab)*)* = b(ab)*.
Problem 6. Let ? = {?, ?, ?, ?}. Define ? on ? as follows: ? = {(?, ?), (?, ?), (?, ?), (?, ?), (?, ?)}. (b) Find the symmetric closure of R.
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