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3 years ago

Use the set A = { a, b, c ,d } to answer the following questions.

Computers and Technology

1 answer:

Gekata [30.6K]3 years ago

6 0

Answer:

What is the cardinality of A? 4

What is the power set of ℘(A)?

P(A) = {Ф, {a}, {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c}, {a,b,d}, {b,c,d}, {a,c,d},{a,b,c,d}}

What is the cardinality of the power set? 16

What is the power set of A = { }? => {{ }} or {Ф

Explanation:

Given set is:

A = {a,b,c,d}

What is the cardinality of A?

The cardinality of set is the number of elements in the set

Since, set A has four members the cardinality is 4.

i.e.

n(A) = 4

What is the power set of ℘(A)?

The power set of a set consists of all the subsets of a set.

So the power set of A will consist of all subsets of A.

The power set is:

P(A) = {Ф, {a}, {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c}, {a,b,d}, {b,c,d}, {a,c,d},{a,b,c,d}}

What is the cardinality of the power set?

The number of subsets of a set is the cardinality of power set.

As A is 4 members,

Cardinality of Power set of A = 2^4 = 16

What is the power set of A = { }

As A is an empty set, its power set will have only one element (Ф) as member

P(A) = {{ }} or {Ф}

Hence,

What is the cardinality of A? 4

What is the power set of ℘(A)? P(A) = {Ф, {a}, {b}, {c}, {d}, {a,b}, {a,c}, {a,d}, {b,c}, {b,d}, {c,d}, {a,b,c}, {a,b,d}, {b,c,d}, {a,c,d},{a,b,c,d}}

What is the cardinality of the power set? 16

What is the power set of A = { }? => {{ }} or {Ф

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Answer:

#include <iostream>

#include <string>

#include <cstring>

#include <cstdlib>

using namespace std;

struct Person

{

string name;

int age;

};

int main()

{

struct Person data[10];

struct Person *pData[10],*temp;

string names[] = {"a","b","c","g","z","l","p","q","r","w"};

int num[] = {4,6,34,8,13,90,33,22,18,23};

for(int i=0;i<9;i++)

{

data[i].name = names[i];

data[i].age = num[i];

pData[i] = &data[i];

}

for(int i=0;i<9;i++)

{

for(int j=i+1;j<9;j++)

{

if(pData[i]->name.compare(pData[j]->name)>0)

{

temp = pData[i];

pData[i] = pData[j];

pData[j] = temp;

}

for(int i=0;i<9;i++)

{

cout<<pData[i]->name<<" "<<pData[i]->age<<endl;

}

Explanation:

The line #include <iostream> initializes the program.

This program created an array of only 10 structures, Customer data. Also defined an auxiliary array Customer *pData.

The program uses these parameters to sorts the array of pointers so that when you go through pData in increasing order of index k, the entries pData[k] point to Customer objects in decreasing order by balance, meaning that pdata[0] now points to the customer with the highest balance, and pData[9] points to the customer with the smallest balance.

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3 years ago

This program will store roster and rating information for a soccer team. Coaches rate players during tryouts to ensure a balance

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Answer:

import java.util.Scanner;

public class TeamRoster {

public static void main(String[] args) {

Scanner scan = new Scanner(System.in);

int[][] players = new int[5][2];

boolean keepAlive = true;

char input;

for (int i = 0; i < 5; i++) {

System.out.println("Enter player " + (i+1) + "'s jersey number: ");

players[i][0] = scan.nextInt();

if( players[i][0] >= 0 && players[i][0] < 100 ) {

System.out.println("Enter player number less than 100");

System.out.println("Enter player " + (i+1) + "'s rating: ");

players[i][1] = scan.nextInt();

if ( players[i][1] >= 1 && players[i][1] <10 ) {

System.out.println();

} else {

System.out.println("Enter player " + (i+1) + "'s rating: ");

players[i][1] = scan.nextInt();

}

System.out.println();

outputRoster(players, 0);

while (keepAlive) {

outputMenu();

input = scan.next().charAt(0);

if (input == 'q') {

keepAlive = false;

break;

} else if (input == 'o') {

outputRoster(players, 0);

} else if (input == 'u') {

System.out.println("Enter a jersey number: ");

int jerseyNum = scan.nextInt();

System.out.println("Enter a new rating for the player: ");

int newRating = scan.nextInt();

for (int l = 0; l < 5; l++) {

if (players[l][0] == jerseyNum) {

players[l][1] = newRating;

}

} else if (input == 'a') {

System.out.println("Enter a rating: ");

int rating = scan.nextInt();

outputRoster(players, rating);

} else if (input == 'r') {

System.out.println("Enter a jersey number: ");

int jerseyNum = scan.nextInt();

boolean exists = true;

for (int l = 0; l < 5; l++) {

if (players[l][0] == jerseyNum) {

System.out.println("Enter a new jersey number: ");

players[l][0] = scan.nextInt();

System.out.println("Enter a rating for the new player: ");

players[l][1] = scan.nextInt();

}

return;

}

public static void outputRoster(int[][] players, int min) {

System.out.println(((min>0) ? ("ABOVE " + min) : ("ROSTER")));

int item = 1;

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if (player[1] > min) {

System.out.println("Player " + item + " -- Jersey number: " + player[0] + ", Rating: " + player[1]);

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System.out.println();

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public static void outputMenu() {

System.out.println("MENU");

System.out.println("u - Update player rating");

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System.out.println("r - Replace player");

System.out.println("o - Output roster");

System.out.println("q - Quit\n");

System.out.println("Choose an option: ");

}

Explanation:

The program is written in Java.

It is a bit straightforward.

The Scanner module is declared and used to collect input from the user.

The program prompts the user for each player jersey then rating.

All five players details are collected.

The program shows the output of all the entries.

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