Programming Questions and Answers January 29, 2021

2. Write the maximum number of users for each of the following IPv4 networks. . 190.168.1.0255.255.240.0 10.1.1.0255,255.255.0 . 192.0.2.022 198.51.100.0255.255.255.128

(a) Use the law of extensionality to prove that (ANB) x C (A x C) n(B x C) (b) The Boolean sum of product of a function f(x, y, z) is xyz xyz xyz xyz i. Use Karnaugh map to find a minimal form of f(x, y, z) ii. Draw the Boolean circuit which gives the minimal form of f(x, y, z) as output.

1. Suppose we have a sequence of integers 10, 2, 8, 15, 20, 3, 30, 19, 18, 7, 9. Insert these integers into an AVL tree. Which of the following AVL trees are correct 2 8 9 10 15 19 18 20 30 9 10 10 15 19 18 20 30 (a) (b) 2. Use the examples in Problem 1 and 2 to explain the advantage of AVL tree versus BST. Activate Windows Go to Settings to

Suppose the adjacency matrix of a directed graph with weights is a b c d e f a 063000 b002500 c000340 d000023 e 000005 600000 1. Find the shortest path tree from a. Write down the adjacency matrix of the shortest path tree. 2. Now we change the original digraph into undirected one by ignoring the direction of edges. Find out the minimum spanning

Suppose we have an adjacency matrix of a graph as follows 0 1 1 0 0 0 0 1 0 0 1 1 00 1 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0101 0 0 1 0 0 1 0 a b d 0 0 e f g 1. If we use a depthfirst traverse to the graph, what is the order of the traversal. 2. If we use a breadthfirst traverse to the graph, what is the order of the traversal.

Draw the symbol table for the above code using lexical scoping while compilation is taking place. b. What will be printed on screen using the lexical scope Draw the environment for the same code during execution. d. What will be printed on screen using the dynamic scope Activate Go to Settin,include int a,b int p() int a, p a 0 b 1 p 2 return p

Draw a pseudocode which allows users to enter 10 exam scores. The flowchart will a. count and display the number of passing scores (50) and failing scores ( 50). b.I display lowest passing score.

Write an interface named electricity Bill that will calculate and print bills for the city power company. The rates vary depending on whether the use is residential, commercial, or industrial. A code of R means residential use, a code of C means commercial use, and a code of I means industrial use. The rates are computed as follows R RM6.00 plus

Wireless networks are specified in which of the following IEEE standards 1 a. IEEE 802.2 2) b. IEEE 802.3 3 4. c. IEEE 802.5 d. IEEE 802.11

A local area network (LAN) is 1 2 a. a group of computers connected over an expansive geographic area. 4 b. another name for a peertopeer network. 3 c. a group of computers connected within a confined geographic area. d. another name for a serverbased network.

Study the below Java code. Slass Rectangle void draw() class Circle extends Rectangle Override void draw() I. II. III. System.out.println(Rectangle class is running) class yetAnotherClass, extends AnotherClass Override System.out.println(Circle class is running) class TestClass( void displayName() System.out.println(This is qvecciden

Read the following codes and then answer questions int binsrch (int a, int x, int low, int high) the low and high are the first and last indexes of a int mid if (low high) return (1) mid (low high) 2 return (x a mid mid x amid binsrch (a, x, low, mid 1) binsrch (a, x, mid 1, high)) 1. What are the purpose of the function 2. Explain why

The motion of a frictionless Foucault pendulum is described by the system of two equations x 2w sin(a) y kx 0, y 2wcos (a)x ky 0, where a is the latitude of the place where the pendulum is located, w 7.29 x 105 sec is the angular velocity of the Earth, k gl with g 9.8 msec and I is the length of the pendulum. Assume that the pendulum at

1. Consider the problem of scheduling n jobs of known durations t1, ..., tn for execution by a single processor. The jobs can be executed in any order, one job at a time. You want to find a schedule that minimizes the total time spent by all the jobs in the system. (The time spent by one job in the system is the sum of the time spent by this job

Recall that, we will look at an alternative proof for NPcompleteness of VERTEXCOVER. VERTEXCOVERG, k) G (V, E) is an undirected graph that has a vertex cover of size k. A vertex cover is a subset S of V such for each each edge e (u, v) EE at least one of u, v is in S. a) (3 points) Prove that VERTEXCOVER E NP. b) (7 points) Prove that

we will prove that the language ALLTM (M) M is a TM such that L(M) for some alphabet is not recognizable or coTuring recognizable. We will use the language ATM (M,w) M is a TM and M accepts w for this purpose. a) (4 points) Give a mapping reducibility from ATM to ALLTM In other words, prove that ATM SM ALLTM b) (2 points) Based on part a)

Eliminate all useless productions from the grammar SaSABA, A bA, B AA. What language does this grammar generate

Which of the following could be false where L is decidable and L2 is recognizable A. L L is recognizable. B. L L is recognizable. C. (L L2) is recognizable. D. LUL is recognizable. E. None of the above.

Write A C program that ask the user to enter an array 3 3, which include the following functions 1 A function named DiagSum() to find the sum of both main and secondary diagonal elements for the array. 2 A function named Middlearray() to displays the elements of middle row and the elements of middle column of the array. 3 A function named

B) else return B; return A; int">

What does the following program print int ge (int A, int B) if (AB) else return B return A int frec(int D, int v) if (v 1) return D0 return ge (D v1), frec (D, v1)) int main() ( C O O int D1 (5, 32, 12, 7, 9, 112, 98) int v sizeof (D) sizeof (D0) cout frec (D, v) return 0 12 None of these options 9 5 112

Wireless LAN (WLAN) network deployments are on the rise and are becoming increasingly popular because of the ease of deployment, cost effectiveness, scalability, and significant productivity gains. This rise in the recent years has offered greater mobility to users by allowing them to move freely without tangling with wired workstations. Some of

(A) Write the following equation as a C expression and state the order of evaluation f cos(2x)e3x log x x2 (B) use C program to write the following table using for control structure 1 2 2 4 4 16 8 64 16 256 32 1024

if x(n) 0.5u(n) 8(n), Find Z transform and ROC for the following 1) x(n) 2) x(n) 3) x(n4)

You are an operations manager for a company called ZA Fabrics, a manufacturer of two types of fabrics, Linen and Silk, in Johannesburg. The company is currently planning its production schedule for the next month and needs to determine how many units of Linen and Silk it should produce to maximize profit. The profit per meter of Linen is R30, and

A relation R is horizontally fragmented into two sub relations say f1, f2 Then further these two sub relations are vertically fragmented into two sub relations i.e. fl is subdivided into fla and flb, and f2 is subdivided into f2a and f2b. a) Write a relational algebraic query to reconstruct it to the original relation EID F2B) What type of

write a CCJavaPython program to implement KernighanLins bi partitioning algorithm. The objective is to minimize the number of edges in the cut. Input A text file describing a set of even number of nodes and a set of edges. If there are n nodes, the node indices are continuous integers from 1 to n. Input file format The first line has two numbers

Consider the following search problem, represented as a graph. A is the start state and G is the goal. The number beside each edge is the transition cost. Find the cost of the path to the goal using Depth First Search with full duplicate detection, which explorer Children in lexicographical order. 10 Select one O a. 16 O b. 11 c. 9 d. 14 B 2 3 3 D

A text file describing the graph in Fig. 1 is given below 5 1, 10 8, 10 10,8 7,4 3,1 0,1,10 1,2,5 2,3,25 0,3,3 3,4,8 VO V4 10 V3 VI S Figure 1 Example of a weighted undirected graph.,Write a program with the following requirements 1. Your program should read the information of a weighted undirected graph G (V, E) using a text file in the

Perform the Uniform Cost Search (UCS) algorithm on the following graph with path costs (Initial node is S and Goal node is G) and mention its application. (5 marks) 2 C 5 A R D S 8 G 3 5 B E 7 F

1. Define BFS and DFS. Give algorithms for both. Demonstrate the BFS and DFS for the below graph using the explicit data structures.

Write ONE C Program which has four functions and a main as described below 1 5 9 1. (10 Points) A function called funl that takes as input a 2 D matrix of integer values, the number of rows, and number of columns of the matrix, and returns the product (multiplication) of all the elements of the matrix. 2. (10 Points) A function called fun2 that

5. Assume a main memory has the following hex values in the first two bytes Byte 0 8E Byte 1 01 What is the actual decimal value stored in these bytes, assuming they are in 16bit 2s complement representation and the machine is using a) Big endian scheme b) Little endian scheme

There are n players standing around in a circle. Carol, who is not one of the n players, goes around the circle clockwise and taps the head of every second person still standing. As soon as a player has their head tapped, that person sits down. Carol keeps going around the circle until only one person is left standing. and that person is declared

In the Figure besides, if the local preference for Router C is set to 190 and for Router D set to 150, what would be the best path to reach network 170.10.0.0 from AS 256. AS 100 Router 1.1.1.2 Router C 128.213.11.1 170.10.0.0 IBGP AS 300 Router B 128.213.11.2 3.3.3.4 3.3.3.3 Router D AS 256 AS 34 54502

For topology in Figure 3, determine the best path From RTA to Network 180.10.0.0 if RTA receives updates from RTB, RTC and RTD, for the following cases A. If the default configuration used. B. If the (bgp alwayscomparemed) command is configured on RTA. Metric0 RTA 170.10.0.0 2.2.2.2 2.2.2.1 RTC AS 100 180.10.0.0 Set metric 120 1.1.1.1 METRIC

In the context of BGP route selection, a router in an Autonomous System AS1 learns multiple routes to a destination in AS2 in Fig. 3. AS1 AS3 AS100 AS2 Figure 3 BGP (i) List the paths learned by the router in AS1 to AS2. (ii) How can an operator control outbound traffic from AS1 Give an example of how this can be achieved. (iii) Which type of

We saw how BGP routing can be formulated as a game where the selfish players are autonomous systems (ASes), and we saw a case where this game has no Nash equilibrium (stable state). That is, the control plane will keep switching routes even though the physical network is stable. In this problem, well see an example where there are two equilibria,

1. Write a program in MARIE assembly language to perform following code segment. Test your code thoroughly using MARIE simulator with values of X10, X20, and X30. What is the value stored in X and Y by the end of execution Include comments for each line of instruction in your program (12 points). X 10 Y 0 while X 0 do Y X 1 HN endwhile X X 2

Translate the following into colloquial English. 6. (Blank (Folly, 200) Blank (Silly, 200)) 7. Owned (Claire, Silly, 200) Owned (Claire, Folly,200) 8. (Erased (Max, Silly, 200) Erased (Max, Folly, 200)) QUESTION 2 20 1. Demonstrate that P v(Pq) is a tautology. (i) Use a truth table Use logical equivalence (3) (3) (3) (4) (4) 2. Show that(P v P q))

2010365232023117lowing classes Register, Payment and SaleLineltem. Consider the below diagram with the domain model having the with 4202017620 Register makePayment) L 2 x 3 8652320231104202017b2010863 ineltem 231 202017b20 addSale() addPayment) 62320231104202017b2010865232023 addSaleLine Item() 20231104202017b201086523202 2020171 a) Suggest a

Which command could be used to access the value of the key name childone name Ali, birthcity Mecca, birthdat e 112021 name child one childonename childonename

What is the value of the variable num numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 num numbers 02 (1, 3,5,7,9) (2,4,6,8, 10) C(1,2, 3, 4, 5, 6, 7, 8, 9, 10) None of the answers 4

Information Security Retrieval and Awareness (ISRA) model can be used by industry to enhance information security awareness among employees. A common body of knowledge for information security that is suited to industry must be separated into technical information security issues and nontechnical information security issues. Referring to the

Given the formula 3x Vy (R(x, y) R(y, x)) does the model M below satisfy it Explain your answer. A a, b, c, d RM (a, b), (a, c), (b, a), (b, b), (b, d), (c, b), (d, a)

include using namespace std int main () int stop int result int a int b cin stop result 0 for (a 3 a 6 a) for (b 0 b 4 b) if resulta cout result cout stop) ( break (result stop) break return 0 Input 14 Output

Complete the frames (1 2) given below with appropriate port, IP and MAC addresses. Frame 1 is intended for Host 5 for sending a message from Host 1. Frame 2 is coming from the Email server to Host 5. Assume that Mac addresses are Uppercase Letters, and logical addresses are lowercase letters. For Port Address, use Dynamic Port address, for the

Find the shortest path using Dijkstras routing algorithm from source node A to remaining vertices in the following graph S 5 2 a b 2 1 2 C 3 d 1 2 e

Write the equations of the RLC circuit given below. Model with simulink blocks so that the input is v(t) and the output is vc(t). i(t) L R vc(t)

Write a Matlab program that finds the sum of 1235...1052. Question 3 15 points Write down the Matlab code that finds the solution of the differential equation given below. dy 4y(t) et, dt y(0) 1.

Consider the CFG G given in problem 1. Suppose the pumping length for G is 5. Which of the following represents a valid way to break s 0001110011 into u,v,x,y,z according the the pumping lemma In other words, if the vand y are pumped, then the resulting string will always be in L(G). Select all that apply. (00) (0) (11) (1) (0011) () (0) (0011)

The following signal is drawn using a multitransition line encoding technique where 3 transition rules and 3 levels are used. i. Decode the bit stream from it. ii. Encode it using Bipolar AMI encoding, apply any appropriate Scrambling method to get rid of the consecutive 0 problem if there is any. 1

Consider the table below Test1 True True False False False True Test2 True True False True False True Test3 False True True True True True Class a. Define the information gain (i.e. reduction of entropy) of a feature F given a set of examples S. Explain all symbols you use. 2 marks b. Calculate the information gain for each feature in the table

iii. Given the following program segment int x, y 0 for (x0 x

I. II. Find the frequency and time period of the given signal before transmission. Can you relate any kind of transmission impairment with the scenario in the given figure after transmission Justify your answer. 10 ns After Transmission 10 ns Time Time

A sequential circuit has two JK flipflops A and B and one input x. The circuit is described by the following flipflop input equations JAX KA B. JB X, KB A (a) Derive the state equations A(t1) and B(t1) by substituting the input equations for the J and K variables (b) List the state table for the sequential circuit (c) Draw the state diagram of the

The server sends the SYN segment, with the sequence number 4529, the acknowledgment number 1052, and window size 1800. The sizes of Segments 1, 2, 3, and 4 are 192, 262, 831, and 332 respectively. Answer the following questions if the GoBackN protocol is used, I. Determine the sequence and the acknowledgment number of the 2nd segment sent by the

a) Create a Birthday Reminder program that keeps track of birthdays for all of your friends. You must allow the user the ability to add data for a new friend or modify the data for an existing friend. Additional Requirements 1) Create a struct for Date that stores entries for month, day, and year. 2) Create a struct for Friend that stores entries

Q1: create a function that displays each character of this string on the screen with a space between each letter. The string must appear on one line Example output: H e l l o W o r l d , I ' m a n e w j a v a s c r i p t p r o g r a m m e r const stringData = "Hello World, I'm a new javascript programmer"; Q2: Replace all of the pipe "|"

Does the following resource allocation state have a deadlock R. 2 P Why or why not Explain.

Write a java program. Extend the class BinarySearchTree by adding a public method displayItemsInRange (l, w) that outputs in ascending order of node value, all the nodes in a BST whose values, v lie in the range l < v < w . Use recursion and avoid entering any subtrees that can't contain any elements in the desired range. You must also write a

using the code Random rnd = new Random(); rnd.Next(0,1000);

Develop an application that has the computer randomly guesses a number. See the UI below. When the user enters in a 3digit integer and clicks Randomly Guess button, the program continually generates a random integer between 0 and 1000 until it finds the number that the user entered. Randomly Guessing a Number Enter in an 3digit integer 234

Assume a liked list data structure of any size. You can consider the following linked list data structure as an example.

Top 4000 12 4000 6000 4008 6000 5000 6008 18 5000 3000 5008 20 3000 Last 3000 0 3008 a) The value 15 is your current node. Enter a node after 15. What is the complexity (search) of this operation Please demonstrate justify your answer. b) The value 18 is your current node. Enter a node before 15. What is the complexity (search) of this

What is the output of the following Java program 1 public class Exam 2 3 4 5 6 9 10 11 12 13 14 15 16 17 18 19 20 21 2233258 24 public static void main(String args) Count myCount new Count 10 for (int i 0 i 10 i) increment (myCount i) public static void increment (Count c) c.count Count.times System.out.println(myCount 9.count Count,

Use Monte Carlo Method to estimate the following integral. 1 L 1 (x sin (x)) dx Write Python code with n 106. Use the random seed 0. Question 2. Use composition approach to simulate the following distribution P 0.3p1 0.7p2, where p follows a geometric distribution with mean 2 and p2 follows a Bernoulli distribution with mean 0.1. Write Python

1. Use Monte Carlo integration to estimate the following integrals. Compare with the exact answer, if known and compute the error as the absolute value of the difference between the values obtained. 3x x dx, sinx dx , ex dx, ex dx e dx, ex dx, So sin(ex) dx. 2. Use Monte Carlo integration to estimate the following double integral 5e(xx) (xy)dxdy .

Design a program in pseudocode and Flowgorithm that calculates 10 using a While loop. Recall that a factorial is each number multiplied by the previous down to 1 1010 9 8 7 6 5 4 3 2 1 3,628,800 When the design is complete, program the design in Python. Upload the pseudocode and Flowgorithm (.frpg) designs and the Python code.,Design a program in

Design a program in pseudocode that prompts the user to enter a number within a range of 1 to 10. The program should then display the Roman Numeral version of that number. Rules . W Main is the controller. Use Case statements to do the translation from number to Roman numeral. Recall how pseudocode case statements are translated to Python. After

Design a program that asks the users for the length and width of a rectangle. The program should then . Calculate and display the area of the rectangle Tell the user which is larger, the length or width (or are they equal a square). Once designed, build the program in Python. There should be separate modules to get the input, calculate and

Apply a divide and conquer based strategy to approximately calculate the value of the following mathematical equation. Provide a pseudocode to solve the problem. 4 2

1. A system has Five processes (P1, P2, P3, P4 ,P5) and Four reusable resources (R1, R2, R3, R4). There are three instances of R1, two instances of R2 ,one instance of R3 and two instances of R4. The allocation of resources for the five processes in the system are given as follows P1 holds an instance of R1 and is requesting an instance of R2.

A perceptron structure and the training data are given below. Assume the following weights and bias. w1 0.41, w2 0.23, w3 0.5 and b 0.01. TITUTE OF T SCIENC (a) Compute the output y of the perceptron for the first training example. (b) Compute the error. (c) Update the weights and bias. (d) Using the updated parameters, compute the output

(b) T You work in an Information Technology (IT) department in a small company. the IP address given to the company is 195.139.10.0. You are required to install at least three (3) Local area networks (LAN) with a minimum number of 20 hosts in each LAN. Determine the option (1) 6 UTM UT (1) (111) The subnet mask used. UTM UTMwing specification for

Consider the following network structure and the initial weights and bias a given. w1 0.3, W12 0.4, W21 0.3, W22 0.05, W3 0.5, WA 0.2 and bias 0. Given that x1, x2, y 1,0,0.5 . x1 X2 W11 W12 W21 W22 W3 WA y (a) Compute the forward propagation and generate the output. Use Sigmoid activation function. (b) Compute the RMSE loss. (c) Let the

Consider an error function (W 3) (w 4) (w3) (w 4) 4 9 6 . Different variants of gradient descent algorithm can be used to minimize this error function w.r.t (w, W2). Assume (w, W) (1, 1) at time (t1) and after update (w, W2) (1.5, 2.0) at time (t). Assume a 1.5, B 0.6, n 0.3. 1. E(W, W) 0.05 Compute the value that minimizes (w1 , w2).

Consider the following nonlinear equation f(x) x 2x 2x 1 0 1. Solve for the root using interval halving with x 0 and x 1 2. Solve for the root using false position with x 0 and x 1 0 3. Solve for the root using fixed point with xo 4. Solve for the root using Newtons method with Xo 1 Activate Wir

Use the substitution method to show that each of the following recurrences defined on the reals has the asymptotic solution specified (a) (b) T(n) 2T (n2) n has solution T(n) T(n) 2T (n3) O(n) has solution T(n) (n lgn). (n).

2. Draw the computational graph for the equation 1 f(w, z) 1 e(worowx1w) Assume that wo 2,01, W 3,2 and w 3. Using the computation graph show the computation of the gradients also.

A 6 DAB B DA CD B ADC 5 3 3 C 6 7 Which of the following is correct 1 25 1 3 9 8 9 8 6 15 2 B 7 L4 3 4 61 8 10 1 4 7 9 2 5

What is the output of the following code include using namespace std int Twist(int u) int main() int N 10, 9 9 Twist (N) cout

24 A rectangle is defined by 1 2 4 4) Find the transformed coordinates after the following transformation. a) 45 rotation about origin. b) Reflection about line y X.

6. 7 7 7 5 (5 7 9 11 11) Find the transformed coordinates after the following transformation. A polygon is defined by a) 30 rotation clockwise about a point P (2, 2) b) Reflection about line x y.

Give the prefix and postfix expressions corresponding to the binary express tree in the following OO e Prefix ab c d e. Postfix a b c de . Inorder abcde Prefix a b c d e. Inorder a b c d e. Postfix a bcde Inorder a b c d e. Postfix a b c d e. Prefix a bcde Postfix a b c d e. Prefix a b c d e. Inorder abcde

Algorithm 1 Design the Newtons algorithm to determine the roots of the following nonlinear equation (x2) 4x 8 0 when x is in the range 0,4. The output of the algorithm should be a table that presents the following values k, xk, f(xk), f(xk) and hk. For your algorithm, use a convergence tolerance of le5. Algorithm 2 Design the Newtons method to

Given the following formula convert it to java programming language, use the java function table and modular structure. Make sure to declare all your variables. Formula ex Mth.exp(x) cosine (x) Mth.cos(x) show all your steps, Math.sqrt(x) Math.abs(x) Ye Zant e2brt cosine (2nft)

5. Write a python program that displays the following pattern on the console. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (1, 2, 3, 4, 5, 6, 7, 8, 9 1, 2, 3, 4, 5, 6, 7, 8 1, 2, 3, 4, 5, 6, 7 1, 2, 3, 4, 5, 6 1, 2, 3, 4, 5 1, 2, 3, 4 1, 2, 3 1, 2 1

Convert the following C code into equivalent ARMv8 code. Values of a, b are in registers X1, and X2 respectively. Array v holds 64bit integers. The base address of array v is in XO. if (a b) va b1 else va vb 1,Write the value 13 as a 32bit 2s complement number. Give your answer in hexadecimal. (First determine the binary pattern for 13 as a

3. What does the following program print public class Q1 Practice public static void main (String args) int array new int 10, 5, 0, 5, 10 loops (3, array ) public static void loops (int n, int a) for (int i 0 i

5. Consider the transition table 01 B JA A C D B DA D F G E F G G D Construct the minimum state equivalent DFA using partition method. A B C D E F G H

For all parts of this question, you must simplify your answer to get full marks. An answer is only fully simplified when it contains either no negations or all negations are on individual variables. Show all steps in your simplification. Let P(x, y) be the predicate (x y) (3q Z, xy a) State the converse of P(x, y). b) State the inverse of P(x,

Prove or disprove each of the following statements. You must show your full formal proof for full marks. a) If ab is an even number, then a is even or b is even. b) MER, Vx ER (x(1x) M) c), Vx E R (log x M) d) The sum of all odd numbers from 1 to 2n 1 is n. You must use induction for this proof.

write a program that compares two files. First, the program will read two file names from the user. Next, the program should count how many words in the first file appears in the second. After that it should print a report of the comparison of two files. The following outlines a plan to solve this problem. 1. Create two Scanner objects to read the

Enter the path for the first file input1.txt Enter the path for the second file input2.txt First file has 45 words. 38 of them are found in the second.

Write a function called mysterysum () that takes one integer parameter, n, and calculates a sum as follows For all integers from 1 up to but not including n I For even numbers add the square of the number For odd numbers, add twice the number Signature def mysterysum (n) your code here return result Examples mysterysum (4)) 12 mysterysum (13) )

Write a recursive function named nonmatching that accepts two strings as parameters, and returns an integer representing the number of character indexes between the two strings that do not match. For this problem, two strings are defined as having a match at a given index if they contain exactly the same ASCII character value at that index. For

Create an assembly language program to measure a voltage from a battery (e.g., dry cell) and display the pertinent value on the LCD screen. VOLTMETER 2.4 V Note that the voltage fed to the input of the STM32F411RE processor should not exceed 3.3 volts else, the processor may get damaged. 15 points

Define the set T recursively with Basis step (0,0) T Recursive step if (a, b) e T then (a 1,b2) T and (a 1,61) e T. (a) Give five different elements of T. (b) Is (0.3) in 7 Explain why or why not.,(7) Define the set U recursively with Basis step (0,0) EU Recursive step if (a, b) U then (a 1,b1) EU and (a4, b4) U. Use structural induction to

We consider a team of a 1 engineers that may be allocated to n 1 projects (each engineer can work on at most one project, heshe cannot work parttime on different projects). The nonnegative profit pk(i) brought by project k 1,...,n depends on the number i 0,..., a of engineers that are allocated to it, and is a nondecreasing function of i for

2. Determine if each of the following relations is reflexive, antireflexive, symmetric, antisymmetric, or transitive. Briefly explain your answer for each property, even if the answer is no. (a) (5 points) Relation E is defined on Z such that for any integers x and y, xEy if xy is even. (b) (5 points) Relation O is defined on Z such that for any

To calculate portfolio expected returns given the weights allocated to those assets based on past historical performance we can use the following equation. Select the correct answer 4() Hp E (wr) w I Mp ri ri mp E(wri Swir I . E(wri w (r) Wi w

Let X R(0,0) and consider the relation on X defined by (x1, y1) (x2, Y2) AER s.t. (x1, y1) (x2, Ay2). . (A) Prove that is an equivalence relation. . (B) Give an explicit description of the set P(R) of equivalence classes of . This is called the real projective line. (C) Define a function which is a bijection from P (R) to the unit circle S

2. Use the following schema and query plan to answer the corresponding questions R (a,b,c) B(R) 1000 T(R) 10,000 Min (R,a) 01 Max (R,a) 9000 V(R,b) 100 V(R,c)