Question

Please show the proof that: Either [a]=[b] or [a] *union* [b] = empty set this will...

Please show the proof that:

Either [a]=[b]
or [a] *union* [b] = empty set

this will be proof by contrapositibe but please show work:


theorem: suppose R is an equivalence of a non-empty set A. let a,b be within A

then [a] does not equal [b] implies that [a] *intersection* [b] = empty set

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
show proof with all explanations please!! will give a like. theorem: Suppose R is an equivalence...
show proof with all explanations please!! will give a like. theorem: Suppose R is an equivalence of a non-empty set A. Let a, b be within A. Then [a] does not equal [b] implies that [a] intersect [b] = empty set
Let S = {0,1,2,3,4,...}, A = the set of natural numbers divisible by 2, and B...
Let S = {0,1,2,3,4,...}, A = the set of natural numbers divisible by 2, and B = the set of numbers divisible by 5. What is the set A intersection B? What is the set A union B? Please show your work.
Prove the statements (a) and (b) using a set element proof and using only the definitions...
Prove the statements (a) and (b) using a set element proof and using only the definitions of the set operations (set equality, subset, intersection, union, complement): (a) Suppose that A ⊆ B. Then for every set C, C\B ⊆ C\A. (b) For all sets A and B, it holds that A′ ∩(A∪B) = A′ ∩B. (c) Now prove the statement from part (b)
Please show all steps and explain every line of proof. show that if f:[a,b] -> R...
Please show all steps and explain every line of proof. show that if f:[a,b] -> R is differentiable on a closed interval [a,b] and if f' is continuous on [a,b], then f is lipshitz on [a.b]
. Write down a careful proof of the following. Theorem. Let (a, b) be a possibly...
. Write down a careful proof of the following. Theorem. Let (a, b) be a possibly infinite open interval and let u ∈ (a, b). Suppose that f : (a, b) −→ R is a function and that for every sequence an −→ u with an ∈ (a, b), we have that lim f(an) = L ∈ R. Prove that lim x−→u f(x) = L.
Write down a careful proof of the following. Theorem. Let (a, b) be a possibly infinite...
Write down a careful proof of the following. Theorem. Let (a, b) be a possibly infinite open interval and let u ∈ (a, b). Suppose that f : (a, b) −→ R is a function and that lim x−→u f(x) = L ∈ R. Prove that for every sequence an −→ u with an ∈ (a, b), we have t
Let T be the half-open interval topology for R, defined in Exercise 4.6. Show that (R,T)...
Let T be the half-open interval topology for R, defined in Exercise 4.6. Show that (R,T) is a T4 - space. Exercise 4.6 The intersection of two half-open intervals of the form [a,b) is either empty or a half-open interval. Thus the family of all unions of half-open intervals together with the empty set is closed under finite intersections, hence forms a topology, which has the half-open intervals as a base.
Is there a set A ⊆ R with the following property? In each case give an...
Is there a set A ⊆ R with the following property? In each case give an example, or a rigorous proof that it does not exist. d) Every real number is both a lower and an upper bound for A. (e) A is non-empty and 2inf(A) < a < 1 sup(A) for every a ∈ A.2 (f) A is non-empty and (inf(A),sup(A)) ⊆ [a+ 1,b− 1] for some a,b ∈ A and n > 1000.
Let ~ be an equivalence relation on a given set A. Show [a] = [b] if...
Let ~ be an equivalence relation on a given set A. Show [a] = [b] if and only if a ~ b, for all a,b exists in A.
Show Proof of correctness and state, and solve the Recurrence using the Master Theorem. Let G...
Show Proof of correctness and state, and solve the Recurrence using the Master Theorem. Let G = G(V, E) be an arbitrary, connected, undirected graph with vertex set V and edge set E. Assume that every edge in E represents either a road or a bridge. Give an efficient algorithm that takes as input G and decides whether there exists a spanning tree of G where the number of edges that represents roads is floor[ (|V|/ √ 2) ]. Do...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT
Active Questions
  • Use the information from the following Income Statement to create and Projected Income Statement and solve...
    asked 12 minutes ago
  • An unequal tangent vertical curve has the following elements: g1=-3.25%, g2=75%, total length = 500.00’, length...
    asked 14 minutes ago
  • Please write clear definitions of the following legal terms. Commerce Clause Supremacy Clause Indictment Tort
    asked 18 minutes ago
  • Do you think Moralistic Therapeutic Deism is an accurate reflection of society today? What are relevant...
    asked 23 minutes ago
  • The mean operating cost of a 737 airplane is $2,071 per day. Suppose you take a...
    asked 32 minutes ago
  • Arguments can be made on both sides of this debate about the ethical implications of using...
    asked 38 minutes ago
  • In the Chapter, they mention the idea of strategizing around your cash flows. Why are cash...
    asked 43 minutes ago
  • Company A signed a fixed-price $6,500,000 contract to construct a building. At the end of Year...
    asked 44 minutes ago
  • An unequal tangent vertical curve has the following elements: g1=-3.25%, g2=1.75%, total length = 500.00’, length...
    asked 50 minutes ago
  • In a previous​ year, 61​% of females aged 15 and older lived alone. A sociologist tests...
    asked 1 hour ago
  • Topic: Construction - Subsurface Investigation (Note: Briefly discuss in your own words, 1 paragraph minimum.) Typically...
    asked 1 hour ago
  • What is ethical sourcing? Why do companies engage in this practice? What are the benefits and...
    asked 2 hours ago