Answered: Discrete Math: Let X be the set of…

Discrete Math: Let X be the set of real numbers. Assume that R on X is an equivalence relation. Demonstrate that you can induce a partition on X by grouping all equivalent elements together.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 27E: Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct...

See similar textbooks

Related questions

Q: 6. Prove the following version of the Fundamental Theorem of Calculus: Theorem 1. Let F [a, b] → R…

Q: 39 2-31]2, 2004] 니 dz de where 2 =/ 2₁1 and 12 = [ 2.1 2-√² ] Z

Q: J(n) = J ( 7² ) + J ( ²3 ) + J (7) + n

Q: x f(x) 0,0 1,0 0,5 2,119 1,0 15 20 2,910 3945 5,72 2,5 8,695

Q: Zet U= Span ([]₁[0]) subspace on product of Rs Answer the following questions basal this piven u and…

A: Let be a subspace of .Answer the following questions based on this given U and the use of the dot…

Q: 6. Solve the following problem for u(x,t): ²u du Əx² Ət = subject to the conditions u(2,1) = 1,…

A: The given partial differential equation (PDE) is a heat equation, and you are also provided with…

Q: Consider the following matrix and answer the following questions: A = [11] 6 without doing any…

Q: [X₁ + x₂ + x3 x4 3x1 +5x22x3 + x4 -3x₁7x₂+7x35x4 1+3x2 - 4x3 + 3x4 = 3 = 1 = 7 = -5.

A: The given system of equations

Q: Consider the following stiffness matrix for a three mass, four spring system: K= -(k₂ +k₂) k₂ 0 4)…

A: We have to Find the three natural frequencies of the system and give the ratios of amplitudes,…

Q: An investment is providing a scholarship worth $4720 every year indefinitely. What is money invested…

Q: Use rectangles to estimate the area under the graph of ƒ(x) = 4 − x², above the x-axis and from x =…

Q: Define g: Z × Z → Z, g(x, y) = z, - where z mod 3 = x and z div 3: Find g (1,4). Y.

A: The objective of the question is to find the value of z in the function g(x, y) = z, where z mod 3 =…

Q: 3. Determine whether each of the following sets is a subspace of the vector space Pn(R) of polyno-…

Q: Problem 0.7 Consider the sequence an = { 3 1 n² if n = 1 if n ≥ 2 (1) Show that an = (1 n+1 (2) Use…

Q: -2 5 4 Find the characteristic equation of the matrix 0 -1 -3 002 Your answer must be an equation.…

Q: Using residues, where a > 0 evaluate the integral x sin ax cos ax x² +9 dx

Q: In general, most medical practices would hope to see a no show rate that is 3% or below. As you…

A: The objective of the question is to calculate the no show rate for the medical practice. The no show…

Q: In Problem 11 to 15, write each sentence in symbolic form. Represent each simple statement in the…

Q: Consider the basic feasible solution of a transportation problem given below: 14 12 10 13 True False…

A: A basic feasible solution of a transportion problem is said to be an optimal solution if it…

Q: 4. The series f(x) = ² - can be shown to converge on the interval [-1, 1). n=1 n (a) Find the series…

Q: From the following function, graph in the indicated Interval f(x) = A 2 1-2x + 2π -< X< TT X</ 2 <X<…

A: Given Information:The function is provided as To find:a) The value of as area under the curve.b)…

Q: 7. Let fn [a, b] R be Riemann integrable and suppose that fn →f uniformly on [a, b]. (a) Prove that…

Q: Question: The polynomials p(x) = x(x − 1) and q(x) = ½ (x − 1)(x − 2) are orthogonal when the inner…

Q: Let f(x) = (x² − 3)eª. (x² − 3)e. The function has two critical points at x = -3, and x = 1. (a) Use…

A: (a) We have to Use the second derivative test to classify each critical point as local max or…

Q: Two dice are rolled. Find the odds in favor of rolling the following. (a) A sum of 5 (b) A sum of…

A: The objective of this question is to calculate the odds in favor of rolling a certain sum when two…

Q: it If p(x)=2x²-3x+5, what is the remainder of p(x)+(x-5)? A) -230 B) 0 40 240

A: We, use division algorithm to find remainder.

Q: Let U = {10, 11, 13,14,15,16,17,20} be a universal set, and the ordering of elements of U has the…

Q: For each of the following sets of vectors in R³, determine whether the vectors span R³. For those…

A: 1) a) Let us consider the relation: where are to be determined.…

Q: (a) Let G be a simple graph with n vertices and m edges where m ≥ (^₂¹) + 2. (i) Let vand w be any…

Q: f(x, y) = √ √1 − ² − 2 a) Sketch traces for some values of f(x, y) = k, xz-trace and yz-trace, and…

A: The given function is .Sketch the traces for some values of and also for and as follows.Put as…

Q: / التاريخ : H.W / is 2 = conformal mapping W+2 zi+w D الموضوع : find image for Retzl Sl

A: (.) Given mapping is, We have to find image for under the given mapping.(.) (.)

Q: Consider the inner product space R³ with (u, v) = U₁V₁ +2u2v₂ + 3u3V3 for every π = (U₁, U2, U3)¹, V…

Q: Use the simplex method to solve the linear programming problem. ECOS B. There is no maximum Maximize…

A: Here we have to use the simplex method to solve the given linear programming problem.

Q: Consider the function whose graph is the surface shown at the right. Which traces go with which…

A: From this picture, we can easily get the required traces

Q: Let ƒ : R¹ → Rk be a continuous function. Which of the following claims are true? Justify your…

A: Given that be a continuous function.We know that a function is a continuous function if is an…

Q: Assume you are given recursive algorithms (like search algorithms) that, given large inputs of size…

Q: 39. Let C be the curve of intersection between the cylinder x² + y²-1 and the plane z x. Find the…

A: Given that C be the curve of intersection between the cylinder x2+y2=1 and the plane z=x.We need to…

Q: B = {sin(t), sin(2t), sin(3t), sin(4t)} is an orthogonal set in C( [−â, π] ) with 1 (f,9) = = [**…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Calculate the proximity to each other and the angles of each location using Law of Cosines to each…

A: To calculate the proximity (distance) between two locations and the angles formed by these locations…

Q: Question 3.1. Use integration by parts to solve the given indefinite integral and thus evaluate…

Q: 9. Find the average distance from the origin to a point between the spheres x² + y² + z² = 1 and x²…

Q: Given the N-length sequence x[n]: 10 8 7 6 5 3 2 G find the following values of x[n]: a. [8] =…

Q: Evaluate the line integral, where C is the given curve. Lo (x + yz) dx + 2x dy + xyz dz, C consists…

A: We have to evaluate the following line integral Where C consists of line segments to and from to…

Q: Graph the function f(x) over the given interval. Partition the interval into 4 subintervals of equal…

Q: Learning Target R4 Core: Given a statement to be proven by (weak) induction, I can state and prove…

Q: 2. On a certain day, the depth off a pier at high tide was 6m. After 6h, the depth of the water was…

Q: Find the inverse Laplace transform of 68 +4 8²-4 8>2

A: Given function: We have to find the inverse Laplace transform of the given function.

Q: Exercise 1 (Br(a) is closed). Recall that for a € R" and r > 0, we define Br(a) = B(a, r) := {x € R"…

Q: 2 table. Speedometer readings for a motorcycle at 12-second intervals are given in the t (second) v…

Q: Suppose A is a matrix with eigenvector : = -4] -5 -11- -1 Find the following. A A -2 corresponding…

Question

Discrete Math: Let X be the set of real numbers. Assume that R on X is an equivalence relation. Demonstrate that you can induce a partition on X by grouping all equivalent elements together.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given information

VIEW

Step 2: Proof of Union forming the whole set.

VIEW

Step 3: Proof of Mutually disjoint equivalence classes

VIEW

Solution

VIEW

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

In Exercises 610, a relation R is defined on the set Z of all integers, In each case, prove that R is an equivalence relation. Find the distinct equivalence classes of R and least four members of each. xRy if and only if x2+y2 is a multiple of 2.
Does the relation is a brother of have a reflexive property consider one male? A symmetric property consider two males? A transitive property consider three males?
Prove Theorem 1.40: If is an equivalence relation on the nonempty set , then the distinct equivalence classes of form a partition of .
Let A=R0, the set of all nonzero real numbers, and consider the following relations on AA. Decide in each case whether R is an equivalence relation, and justify your answers. (a,b)R(c,d) if and only if ad=bc. (a,b)R(c,d) if and only if ab=cd. (a,b)R(c,d) if and only if a2+b2=c2+d2. (a,b)R(c,d) if and only if ab=cd.
In Exercises , a relation is defined on the set of all integers. In each case, prove that is an equivalence relation. Find the distinct equivalence classes of and list at least four members of each. 10. if and only if .
In Exercises , prove the statements concerning the relation on the set of all integers. 14. If and , then .