Question: Define a relation R on N x N by R = {(x,y) | x N , y N and x+y is even} Prove or disprove:

Define a relation R on N x N by

R = {(x,y) | x N, y N and x+y is even}

Prove or disprove: R is an equivalence relation.

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 Databases Questions!

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:

Let N = {0, 1, 2, 3,...} be the set of natural numbers. Define a relation R on N N by (a, b) R(c, d) a+d=c+b. (a) Use only the laws of commutativity (a+b=b+a), associativity (a + (b+c) = (a+b)+c)...

Q:

4. N is the set of natural numbers, that is, the integers greater than zero. Define a relation R on N N by R = { (x,y)|x N, y N and x + y is even} Prove that R is or is not an equivalence relation

Q:

. Define a relation R on Nx N by (a, b)R(c, d) if and only if a+b=c+d. Prove that R is an equivalence relation on N x N. Let S denote the set of equivalence classes of R. Show that there is a...

Q:

This Journal entry has two parts: Part A: Select TWO examples of solutions to trig identities from the Content section ( Examples or Check your Understanding ) or from Assignment 1 Solutions....

Q:

Let X and Y be sets. Let N be an equivalence relation on X and let x be an equivalence relation on Y. Let's define a relation R on X X Y by: (x, y) R (x', y') if and only ifx N x' ory z y'. Determine...

Q:

Let X and Y be sets. Let N be an equivalence relation on X and let x be an equivalence relation on Y. Let's define a relation R on X X Y by: (x, y) R (x', y') if and only ifx N x' ory z y'. Determine...

Q:

Let G be a group and H a normal subgroup of G. Define a relation R on G x G by x Ry if and only if ry E H. (a) Show that R is an equivalence relation on G. (b) For a, a, y, bE G: (i) Show that if x...

Q:

6. Let A = {x E Z |x 2 5a + 2 for some integer a}, B = {y E Z | y = 10!) 3 for some integer b}, and C = {z E Z | z = 106 + 7 for some integer C}. Prove or disprove each of the following statements....

Q:

Urylon fibers are used in premium fishing nets because the polymer is relatively stable to UV light and aqueous acid and base. The structure of Urylon is (a) What functional group is contained in the...

Q:

There are Seven (7) Principles of Public Life outlined in the ethical standards (also known as the Nolan Principles) that people working in the public sector are expected to adhere to. Lord Nolan...

Q:

Which of the following types of income is subject to the self-employment tax? Multiple Choice Income from a sole proprietor's coffee shop. Gain on the sale of a home. W-2 income. Interest earned on a...

Q:

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...

Q:

5. Describe the relationship between history and identity.

Q:

9. Identify eight contact conditions that influence positive attitude change.

Q:

1. What are some examples of hidden histories, and why are they hidden?