Write a C++ or Java program that uses bit strings to find A ∪ B, A ∩ B, and A – B given subsets A and B of a universal set with 10 elements {0, 1, 2, 3, 4, 5, 6, 7, 8,9}. You have to use bit string Print to the screen set A, set B ( be sure to print out the name of the sets), as well as the set operation results (be sure to print out the name of the operations). The program requires that elements of subsets A and B are from user input. You can make the assumption that user input numbers are within the domain of the set {0, 1, 2, ..., 9} and there is no improper input. Additional requirements and reminders: • The use of STL, templates, and operator overloading is not permitted in any form. • Remember: You must use a bit string when representing a set. You may not use an array of Boolean variables. • The elements of subset A and subset B must from user input. You may not hardcode the two subsets in your program. Hint: (1) It is a bit easier to program if we construct the bit string of a set from right to left. For example, Let U = {1, 2, 3, 4, 5, 6, 7, 8 }. How would you represent the following sets? A = {1, 2, 6} B = {2, 4, 6, 8} A: 00100011 B: 10101010 (2) How to read elements of a set from user input and save it using a bit string? int setA = 0; // a variable to save the bit string of set A int userInput; // a variable to save the user input // put the following code in a loop to continually read user input and // construct the bit string of set A until encountering an invalid number to stop (e.g. -1) setA |= (1 << userInput); // | is the bitwise-or; << is the left shift operator (3) How to find the set operation results? Take the intersection ∩ as an example. int setA, setB, intersection; intersection = setA & setB; Think about how to print to the screen all elements of a set from a bit string. You may need the right shift operator (>>), the bitwise-and (&), an auxiliary bit string for the purpose of “mask”, and a loop.

Question

Write a C++ or Java program that uses bit strings to find A ∪ B, A ∩ B, and A – B given subsets A and B of a universal set with 10 elements {0, 1, 2, 3, 4, 5, 6, 7, 8,9}. You have to use bit string

Print to the screen set A, set B ( be sure to print out the name of the sets), as well as the set operation results
(be sure to print out the name of the operations). The program requires that elements of subsets A and B are from user input. You can make the assumption that user input numbers are within the domain of the set {0, 1, 2, ..., 9} and there is no improper input.
Additional requirements and reminders:
• The use of STL, templates, and operator overloading is not permitted in any form.
• Remember: You must use a bit string when representing a set. You may not use an array of
Boolean variables.
• The elements of subset A and subset B must from user input. You may not hardcode the two subsets in your program.
Hint:
(1) It is a bit easier to program if we construct the bit string of a set from right to left. For
example, Let U = {1, 2, 3, 4, 5, 6, 7, 8 }. How would you represent the following sets?
A = {1, 2, 6}
B = {2, 4, 6, 8}
A: 00100011
B: 10101010

(2) How to read elements of a set from user input and save it using a bit string?
int setA = 0; // a variable to save the bit string of set A
int userInput; // a variable to save the user input
// put the following code in a loop to continually read user input and
// construct the bit string of set A until encountering an invalid number to stop (e.g. -1)
setA |= (1 << userInput); // | is the bitwise-or; << is the left shift operator
(3) How to find the set operation results? Take the intersection ∩ as an example.
int setA, setB, intersection;
intersection = setA & setB;
Think about how to print to the screen all elements of a set from a bit string.
You may need the right shift operator (>>), the bitwise-and (&), an auxiliary bit string for the
purpose of “mask”, and a loop.