Question: Define a relation on Zas follows: R = {(a, b) : a + b is even }ZZ. List 4 elements in R and then prove

Define a relation on Zas follows: R = {(a, b) : a + b is even }ZZ. List 4 elements in R and then prove that R is an equivalence relation on Z.

please do not prove by example

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 Mathematics Questions!

Q:

In 20X0, Marquette County opened a landfill that was expected to accept waste for four years. The following table indicates the estimates county officials made at the end of each of the four years:...

Q:

What is the probability that a random relation from set A = {a,b, c,d} to set B = {1,2,3,4,...,8} is a one-to-one function? 2. Consider the set A = {1,2,3,4}. On the cartesian product A A we define...

Q:

Intro Group Theory Problem: Let G be a group. (1) Define a relation on G by setting a b if and only if a = b 1 . Use Problem 1 to show that this relation is symmetric. (2) Show that if G has an even...

Q:

Microkernel operating systems aim to address perceived modularity and reliability issues in traditional "monolithic" operating systems. (i) Describe the typical architecture of a microkernel...

Q:

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...

Q:

Use pen and paper answer all the following questions. A) 1. There are five different equivalence relations on the set A={a,b,c}. Describe them all. Diagrams will suffice. 2. Define a relation R on Z...

Q:

Use pen and paper answer all the following questions. A) 1. There are five different equivalence relations on the set A={a,b,c}. Describe them all. Diagrams will suffice. 2. Define a relation R on Z...

Q:

answer the question clearly You are building a flight-control system for which a convincing safety case must be made. Would you assign the tasks of safety requirements engineering, test case...

Q:

In this question assume that p and q are atomic formulae. (a) Compare and contrast path formulae and state formulae in temporal logic. [4 marks] (b) Describe and contrast the meanings of F(G p) and...

Q:

Suppose that R(A, B, C) is a relational schema with functional dependencies F = {A, B C, C B}. (i) Is this schema in 3NF? Explain. [2 marks] (ii) Is this schema in BCNF? Explain. [2 marks] (b)...

Q:

MAT301 ASSIGNMENT 1 DUE DATE: WEDNESDAY MAY 18, 2016 AT THE BEGINNING OF YOUR TUTORIAL Question 1. Define the following relation on the integers: a b 2|(a b) Prove that this is an equivalence...

Q:

C. N. Itall has been a systems analyst for Tun-L-Vision Corporation for many years. When you came on board as part of the systems analysis team and suggested prototyping as part of the SDLC for a...

Q:

Suggest an appropriate independent variable to use in predicting the costs of the following tasks. a. Handling materials at a loading dock. b. Registering vehicles at a county motor vehicle office....

Q:

2. True Or False. Inductive arguments admit of varying degrees of strength and weakness.

Q:

Using the Lambert's model of partnership, how can his be applied to Amazon's partnership with india in 2021 for the provision of medical equipment to tackle covid 19