Question: Set S = {(x,y) RxR:y- x is an integer). a) Prove that S is an equivalence relation on R. b) List four members of [x].

Set S = {(x,y) RxR:y- x is an integer). a) Prove that S is an equivalence relation on R. b) List four members of [x]. c) Which real numbers belong to [-17]

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Accounting Questions!

1. Let R be a relation defined on the set Z by aRb if a

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...

s1 educated (SSE) student for every three public school educated (PSE) students. Reasoning that students are not very dissimilar from threads, he suggests the following entry and exit routines be...

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

This question concerns lexical grammars. (a) Tree Adjoining Grammars contain two types of elementary tree. (i) What are these trees called? [1 mark] (ii) If one were building a grammar for English...

dee complete please help Complexity Theory (a) Defifine the set of Boolean expressions 2CNF and the language 2SAT over them. (b) For a Boolean expression in 2CNF, let G() be the directed graph with...

Porter's Value Chain does not examine departments or accounting cost types, but instead focuses on systems that change inputs into consumer outputs. According to Porter, all businesses are...

Prepare a cash budget for the months of April, May, June, and July, for the following. The ending cash balance in March is 20,000, and the company desires to maintain 10,000 as a minimum cash...

How often do you connect to the Internet? Has this increased or decreased in the past 1 0 years? Do you believe that this trend will continue? How will the way in which they connect to the Internet...

last two options for the multiple choice are : performance management development A construction equipment manufacturer, Roswell Corporation, is focusing on becoming a leader in sustainability in...

5. Try smiling (genuinely) more than you usually doand with people you might not usually smile at. See what happens. Do you feel differently about yourself and others? Do others respond with more...

6. Play with text-to-speech features on your computer. Compare the way the machine reads a passage of text to the way you would read it. Do you have a choice of voices from which to choose, and is...

1. Define and explain culture and its impact on your communication