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 then make 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 to enter 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 A containing n elements to a set B containing m elements. Q2. Implement The Chinese Remainder Theorem. Print the intermediate steps of the Theorem before printing the result of it. Q3. Fuzzy sets are used in artificial intelligence. Each element in the universal set U has a degree of membership, which is a real number between 0 and 1 (including 0 and 1), in a fuzzy set 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, c has a 0.3 degree of membership in A, d has 0.9 degree of 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 an element 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 of membership of an element in SNTis the minimum of the degrees of membership of this element in S and in T. • The difference between two fuzzy sets S and T is the fuzzy set S- T, where the degree of membership of an element in S-T is the minimum of the degrees of membership of this element in S and I minus the degree of membership of this element in T. The union of two fuzzy sets S and T is the fuzzy set SUT, where the degree of membership of an element in S UT is the maximum of the degrees of membership of this element in S and in T. Find the following: 1) AUB 2) B - A
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 then make 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 to enter 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 A containing n elements to a set B containing m elements. Q2. Implement The Chinese Remainder Theorem. Print the intermediate steps of the Theorem before printing the result of it. Q3. Fuzzy sets are used in artificial intelligence. Each element in the universal set U has a degree of membership, which is a real number between 0 and 1 (including 0 and 1), in a fuzzy set 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, c has a 0.3 degree of membership in A, d has 0.9 degree of 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 an element 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 of membership of an element in SNTis the minimum of the degrees of membership of this element in S and in T. • The difference between two fuzzy sets S and T is the fuzzy set S- T, where the degree of membership of an element in S-T is the minimum of the degrees of membership of this element in S and I minus the degree of membership of this element in T. The union of two fuzzy sets S and T is the fuzzy set SUT, where the degree of membership of an element in S UT is the maximum of the degrees of membership of this element in S and in T. Find the following: 1) AUB 2) B - A
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
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Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Transcribed Image Text: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 then
make 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 to
enter 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 A
containing n elements to a set B containing m elements.
Q2. Implement The Chinese Remainder Theorem. Print the intermediate steps of the Theorem
before printing the result of it.
Q3. Fuzzy sets are used in artificial intelligence. Each element in the universal set U has a
degree of membership, which is a real number between 0 and 1 (including 0 and 1), in a fuzzy
set 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, c
has a 0.3 degree of membership in A, d has 0.9 degree
of 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 an
element 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 of
membership of an element in S NT is the minimum of the degrees of membership of
this element in S and in T .
The difference between two fuzzy sets S and T is the fuzzy set S - T, where the degree
of membership of an element in S- T is the minimum of the degrees of membership of
this 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 of
membership of an element in S U T is the maximum of the degrees of membership of
this element in S and in T.
Find the following:
1) A UB
2) B - A
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