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3.5. If U is an ideal of R and 1 ∈ U, prove that U = R.
3.4. Prove that any field is an integral domain.
3.3. If in a ring R every x ∈ R satisfies x2 = x, prove that R
must be commutative
(A ring in which x2 = x for all elements is called a Boolean ring).
3.1. If R is a ring and a, b, c, d ∈ R, evaluate (a + b)(c + d).
3.2. Prove that if a, b ∈ R, then (a + b)2 = a2 + ab + ba + b2 where
by x2 we mean xx.
according to a study conducted by the grade 12 student, php 175 is the average monthly expenses for cell phone loads of high school students in their province.aA statistics students claim that this amount has increased since January of this year .do you think his claim is acceptable if a random sample of 50 students has an average monthly expense of php164 for cellphone loads ? using 5% level of significance , assume that a population standard deviation is 53
A theatre sells seats for shows and needs a system to keep track of the seats they have sold tickets for. Define a class for a type called ShowTicket. The class should contain private member variables for the row, seat number and whether a ticket has been sold or not. Your class should include the following member functions: • a default constructor that initialises the row and seat number to 0 and the sold status to false • an overloaded constructor which accepts as arguments the row and seat number and sets the sold status to false • a member function to check if the ticket has been sold • a member function to update the ticket status to sold • a member function to print the row, seat number and sold status • a destructor. Embed your class definition in a test program which creates some ShowTicket objects, set some tickets as sold, and prints each of them out.
Explain the term ‘opportunity cost’.
1. Let x be a nilpotent element of a ring A. Show that 1 + x is a unit of A. Deduce
that the sum of a nilpotent element and a unit is a unit.
Write a program to remove unnecessary blanks from a text file. Your program should read the text file and copy it to another text file, but whenever more than one blank occurs consecutively, only one blank should be copied to the second file. The second file should be identical to the first file, except that all consecutive blanks have been replaced by a single blank.
Write a program that initialises a vector with the following string values: “what” “book” “is” “that” “you” “are” “reading”. Display the contents of the vector on the screen to the user as a question and read in the name of the book the user is reading (you can decide what it will be). Have the program add the name of the book to the vector, word by word. For example, if I am reading “How to learn C++”, the program should add the words, “How” “to” “learn” “C++”, one by one to the vector. Display the new vector.
#340153 on Dec 2023