Write a C++ program to implement the following with the specified input and output:First: make a menu list as you find suitable, three main options for the questions, and thenmake suboptions for each one to perform the requirements.Second: you must add option to read from a file at the beginning rather than make the user toenter the values to save time. (the file format/order is up to you).Third: submit compressed folder (the code, input file, and PDF for screenshots).Q1. Find the number of of injections (one to one) and surjections (onto function) from a set Acontaining n elements to a set B containing m elements.Q2. Implement The Chinese Remainder Theorem. Print the intermediate steps of the Theorembefore printing the result of it.Q3. Fuzzy sets are used in artificial intelligence. Each element in the universal set U has adegree of membership, which is a real number between 0 and 1 (including 0 and 1), in a fuzzyset S. The fuzzy set S is denoted by listing the elements with their degrees of membership(elements with 0 degree of membership are not listed).For example:A = {0.2a, 0.4b, 0.3c, 0.9d, 0.7e}B = {0. 9a, 0. 6b, 0.5c, 0. 8d, 0.9e}Assume the size of each set is 10 variables(a-j).For the set A, a has a 0.2 degree of membership in A, b has a 0.4 degree of membership in A, chas a 0.3 degree of membership in A, d has 0.9 degreeof membership in A, and e has a 0.7 degree of membership in A.• The complement of a fuzzy set S is the set S, with the degree of the membership of anelement in S equal to 1 minus the degree of membership of this element in S.• The intersection of two fuzzy sets S and T is the fuzzy set SnT, where the degree ofmembership of an element in SnT is the minimum of the degrees of membership ofthis element in S and in T.• The difference between two fuzzy sets S and T' is the fuzzy set S-T, where the degreeof membership of an element in S-T is the minimum of the degrees of membership ofthis element in S and 1 minus the degree of membership of this element in T.• The union of two fuzzy sets S and T is the fuzzy set S UT, where the degree ofmembership of an element in S U T is the maximum of the degrees of membership ofthis element in S and in T.Find the following:1) AUB2) B- A

I have written code for the first one:

irst: make a menu list as you find suitable, three main options for the question ake suboptions for each one to perform the requirements. econd: you must add option to read from a file at the beginning rather than mal ter the values to save time. (the file format/order is up to you). hird: submit compressed folder (the code, input file, and PDF for screenshots) 1. Find the number of of injections (one to one) and surjections (onto function) ontaining n elements to a set B containing m elements. 2. Implement The Chinese Remainder Theorem. Print the intermediate steps of

irst: make a menu list as you find suitable, three main options for the question ake suboptions for each one to perform the requirements. econd: you must add option to read from a file at the beginning rather than mal ter the values to save time. (the file format/order is up to you). hird: submit compressed folder (the code, input file, and PDF for screenshots) 1. Find the number of of injections (one to one) and surjections (onto function) ontaining n elements to a set B containing m elements. 2. Implement The Chinese Remainder Theorem. Print the intermediate steps of

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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