Question: 2 b) Define a relation on RX R as follows: (x1,y1)~(x2, y2) iff x2 + y = x + y 2 (i) Show that

2 b) Define a relation on RX R as follows: (x1,y1)~(x2, y2)

2 b) Define a relation on RX R as follows: (x1,y1)~(x2, y2) iff x2 + y = x + y 2 (i) Show that is an equivalence relation on RX R.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To show that is an equivalence relation on RXR three properties need to be verified reflexive symmet... View full answer

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:

The Tamarisk manufactures double-sided pens-a pen on one side, a highlighter on the other. As the accounting manager, Shade is responsible for presenting three different versions of the company's...

Q:

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...

Q:

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...

Q:

11. (a) Given the set A = {1, 2, 3} and the set S = {(x, y) | x and y in A}. Consider the relation defined on S as follows: ((x1, y1) (x2, y2) if x1 x2 and y1 y2. Draw the directed graph of this...

Q:

This question is giving me a lot of trouble: Given the set A = {1, 2, 3} and the set S = {(x, y) | x and y in A} Consider the relation defined on S as follows: ((x 1 , y 1 ) (x 2 , y 2 )) if x 1 x 2...

Q:

This is topology. 3. [solo] (a) Consider the equivalence relation on R defined by (x1, y1) ~ (x2, y2) if and only if x1 + y1 = x2 + y2. Describe the set of points in each equivalence class. What is...

Q:

Christopher s Custom Cabinet Company uses a job order cost system with overhead applied as a percentage of direct labor costs. Inventory balances at the beginning of the current year follow: Raw...

Q:

APStatistics 3.02 Looking at the Data Directions: Complete the assignment. Clearly label each answer. Your answers for this assignment must include reasons; simply stating the answer without...

Q:

APStatistics 3.02 Looking at the Data Directions: Complete the assignment. Clearly label each answer. Your answers for this assignment must include reasons; simply stating the answer without...

Q:

The following problem must be solved and written in Scheme programming language: 1. Re-write the following arithmetic expressions as Scheme expressions and show the result of the Scheme interpreter...

Q:

The Accounts Payable Clerk receives invoices from vendors. When vendor invoices are received, the Accounts Payable Clerk records the amount due in the accounts payable sub-ledger and files the...

Q:

Given the following ANOVA table: Source DF SS MS F Regression 1 1300 1300.00 24.00 Error 12 650 54.17 Total 13 1950 Requirements: (a) Determine the coefficient of determination. (b) Assuming a direct...

Q:

During the summer months Terry makes and selly necklaces on the beach. Last summer she sold the necklaces for two sales per day. ( a ) Find the demanc function ( price pas a function of units sald x...

Q:

A thermodynamic system undergoes a process in which its internal energy decreases by 500 J. At the same time, 220 J of work is done on the system. Find the energy transferred to or from it by heat.

Q:

A thermodynamic process occurs in which the entropy of a system changes by - 8.0 J/K. According to the second law of thermodynamics, what can you conclude about the entropy change of the environment?

Q:

A thermal window with an area of 6.00 m2 is constructed of two layers of glass, each 4.00 mm thick, and separated from each other by an air space of 5.00 mm. If the inside surface is at 20.0C and the...

Q:

The yellow caution light on a traffic signal should stay on long enough to allow a driver to either pass through the intersection or safely stop before reaching the intersection. A car can stop if...

Q:

The void fraction of a porous medium is the ratio of the void volume to the total volume of the material. The void is the hollow space within the material; it may be filled with a fluid. A...

Q:

A shaft carries five masses A, B, C, D and E which revolve at the same radius in planes which are equidistant from one another. The magnitude of the masses in planes A, C and D are 50 kg, 40 kg and...

Q:

If p > q are primes, a group of order pq has at most one subgroup of order p. Suppose H,K are distinct subgroups of order p. Show H K = (e).

Q:

If : G H is a homomorphism with kernel N and K

Q:

If where a is the image of a under the canonical epimorphism z z P . (a) If is monic and /is irreducible in Z p [x] for some prime p, then f is irreducible in Z[x]. (b) Give an example to show that...

Q:

=+ Do you have any long-term goals?

Q:

=+and take some online quizzes, or try the one at https://testyourself. psychtests.com/testid/3979. Do you think you are emotionally intelligent? Does your performance on the test seem to reflect your

Q:

=+actual experience? What is your opinion of the test you tried? Is there information on the site showing its validity and reliability?